Solve for x x^2-12x+k=5

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Trigonometry

$x^{2} - 12 x + k = 5$

Move $5$ to the left side of the equation by subtracting it from both sides.

$x^{2} - 12 x + k - 5 = 0$

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 1$ , $b = - 12$ , and $c = k - 5$ into the quadratic formula and solve for $x$ .

$\frac{12 \pm \sqrt{{(- 12)}^{2} - 4 \cdot (1 \cdot (k - 5))}}{2 \cdot 1}$

Simplify.

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Simplify the numerator.

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Raise $- 12$ to the power of $2$ .

$x = \frac{12 \pm \sqrt{144 - 4 \cdot (1 \cdot (k - 5))}}{2 \cdot 1}$

Multiply $k - 5$ by $1$ .

$x = \frac{12 \pm \sqrt{144 - 4 \cdot (k - 5)}}{2 \cdot 1}$

Apply the distributive property.

$x = \frac{12 \pm \sqrt{144 - 4 k - 4 \cdot - 5}}{2 \cdot 1}$

Multiply $- 4$ by $- 5$ .

$x = \frac{12 \pm \sqrt{144 - 4 k + 20}}{2 \cdot 1}$

Add $144$ and $20$ .

$x = \frac{12 \pm \sqrt{- 4 k + 164}}{2 \cdot 1}$

Factor $4$ out of $- 4 k + 164$ .

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Factor $4$ out of $- 4 k$ .

$x = \frac{12 \pm \sqrt{4 (- k) + 164}}{2 \cdot 1}$

Factor $4$ out of $164$ .

$x = \frac{12 \pm \sqrt{4 (- k) + 4 (41)}}{2 \cdot 1}$

Factor $4$ out of $4 (- k) + 4 (41)$ .

$x = \frac{12 \pm \sqrt{4 (- k + 41)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{12 \pm \sqrt{2^{2} (- k + 41)}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{12 \pm 2 \sqrt{- k + 41}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{12 \pm 2 \sqrt{- k + 41}}{2}$

Simplify $\frac{12 \pm 2 \sqrt{- k + 41}}{2}$ .

$x = 6 \pm \sqrt{- k + 41}$

The final answer is the combination of both solutions.

$x = 6 + \sqrt{- k + 41}$

$x = 6 - \sqrt{- k + 41}$

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Name

Name	eight hundred six million three hundred thousand two hundred seventy-five

Interesting facts

806300275 has 32 divisors, whose sum is 1293594624
The reverse of 806300275 is 572003608
Previous prime number is 11

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 31
Digital Root 4

Name

Name	four hundred ninety-six million five hundred seventy-two thousand eighty-four

Interesting facts

496572084 has 128 divisors, whose sum is 2067310080
The reverse of 496572084 is 480275694
Previous prime number is 59

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 45
Digital Root 9

Name

Name	one billion seven hundred thirteen million ninety-four thousand four hundred twenty-five

Interesting facts

1713094425 has 8 divisors, whose sum is 1818600960
The reverse of 1713094425 is 5244903171
Previous prime number is 21

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 36
Digital Root 9

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