Solve by Completing the Square x^2-10x-4=0

$x^{2} - 10 x - 4 = 0$

Add $4$ to both sides of the equation.

$x^{2} - 10 x = 4$

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(- 5)}^{2}$

Add the term to each side of the equation.

$x^{2} - 10 x + {(- 5)}^{2} = 4 + {(- 5)}^{2}$

Simplify the equation.

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Raise $- 5$ to the power of $2$ .

$x^{2} - 10 x + 25 = 4 + {(- 5)}^{2}$

Simplify $4 + {(- 5)}^{2}$ .

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Raise $- 5$ to the power of $2$ .

$x^{2} - 10 x + 25 = 4 + 25$

Add $4$ and $25$ .

$x^{2} - 10 x + 25 = 29$

Factor the perfect trinomial square into ${(x - 5)}^{2}$ .

${(x - 5)}^{2} = 29$

Solve the equation for $x$ .

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Take the square root of each side of the equation to set up the solution for $x$

${(x - 5)}^{2 \cdot \frac{1}{2}} = \pm \sqrt{29}$

Remove the perfect root factor $x - 5$ under the radical to solve for $x$ .

$x - 5 = \pm \sqrt{29}$

Remove parentheses.

$x - 5 = \pm \sqrt{29}$

Add $5$ to both sides of the equation.

$x = \pm \sqrt{29} + 5$

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{29} + 5$

Decimal Form:

$x = 10.38516480 \dots, - 0.38516480 \dots$

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Name

Name	eight hundred forty-seven million two hundred ninety-five thousand nine hundred sixteen

Interesting facts

847295916 has 16 divisors, whose sum is 2541887784
The reverse of 847295916 is 619592748
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 51
Digital Root 6

Name

Name	one hundred seventeen million three hundred sixty thousand seventy-nine

Interesting facts

117360079 has 4 divisors, whose sum is 121145920
The reverse of 117360079 is 970063711
Previous prime number is 31

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 34
Digital Root 7

Name

Name	six hundred twenty-nine million eight hundred thirty-eight thousand five hundred twenty

Interesting facts

629838520 has 64 divisors, whose sum is 2566521936
The reverse of 629838520 is 025838926
Previous prime number is 163

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 43
Digital Root 7

Factor x^2-4

Solve by Completing the Square x^2-10x-4=0

Solve Using the Quadratic Formula 2x^2-7x=1

Evaluate 6/4

Expand using the Binomial Theorem (x-y)^2