To remove the radical on the left side of the equation, square both sides of the equation.

Simplify the left side of the equation.

Simplify the right side of the equation.

Rewrite <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mn>2</mn><mo>-</mo><mi>y</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> as <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>2</mn><mo>-</mo><mi>y</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><mo>-</mo><mi>y</mi><mo>)</mo></mrow></mstyle></math> .

Expand <math><mstyle displaystyle="true"><mrow><mo>(</mo><mn>2</mn><mo>-</mo><mi>y</mi><mo>)</mo></mrow><mrow><mo>(</mo><mn>2</mn><mo>-</mo><mi>y</mi><mo>)</mo></mrow></mstyle></math> using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> by <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>2</mn><mi>y</mi></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn><mi>y</mi></mstyle></math> .

Since <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> is on the right side of the equation, switch the sides so it is on the left side of the equation.

Move all terms containing <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> to the left side of the equation.

Subtract <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn><mi>y</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>4</mn><mo>+</mo><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mn>5</mn><mi>y</mi></mstyle></math> using the AC method.

Consider the form <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi></mstyle></math> . Find a pair of integers whose product is <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> . In this case, whose product is <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and whose sum is <math><mstyle displaystyle="true"><mo>-</mo><mn>5</mn></mstyle></math> .

Write the factored form using these integers.

Set <math><mstyle displaystyle="true"><mi>y</mi><mo>-</mo><mn>4</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

Set the factor equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to both sides of the equation.

Set <math><mstyle displaystyle="true"><mi>y</mi><mo>-</mo><mn>1</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and solve for <math><mstyle displaystyle="true"><mi>y</mi></mstyle></math> .

Set the factor equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to both sides of the equation.

The solution is the result of <math><mstyle displaystyle="true"><mi>y</mi><mo>-</mo><mn>4</mn><mo>=</mo><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mi>y</mi><mo>-</mo><mn>1</mn><mo>=</mo><mn>0</mn></mstyle></math> .

Exclude the solutions that do not make <math><mstyle displaystyle="true"><msqrt><mi>y</mi></msqrt><mo>=</mo><mn>2</mn><mo>-</mo><mi>y</mi></mstyle></math> true.

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