What are the solutions to the equation x^2-12x=-24 ?

The solutions to the equation x^2-12x=-24 are x=2(3+sqrt(3)),x=2(3-sqrt(3))

Find the zeros of x^2-12x=-24

The zeros of x^2-12x=-24 are x=2(3+sqrt(3)),x=2(3-sqrt(3))

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x^{2} - 12 x = - 24

x = 2 (3 + 3), x = 2 (3 - 3)

Decimal Notation

x = 9.46410 \dots, x = 2.53589 \dots

Solution steps

x^{2} - 12 x = - 24

Move

24

to the left side

x^{2} - 12 x + 24 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 1 \cdot 24}{2 \cdot 1}

(- 12)^{2} - 4 \cdot 1 \cdot 24 = 43

x_{1, 2} = \frac{- ( - 12 ) \pm 4 3}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 12 ) + 4 3}{2 \cdot 1}, x_{2} = \frac{- ( - 12 ) - 4 3}{2 \cdot 1}

x = \frac{- ( - 12 ) + 4 3}{2 \cdot 1} : 2 (3 + 3)

x = \frac{- ( - 12 ) - 4 3}{2 \cdot 1} : 2 (3 - 3)

The solutions to the quadratic equation are:

x = 2 (3 + 3), x = 2 (3 - 3)

x^{2} - 12 x = - 10

4 x^{2} - 7 x - 1 = 0

2 x^{2} - 27 x + 12 = - 10 x - 19

x, x^{2} + y^{2} + 8 x - 6 y + 30 = 0

(2 x + 4) (2 x - 4) = (x - 8) (x + 3) + 6

What are the solutions to the equation x^2-12x=-24 ?
The solutions to the equation x^2-12x=-24 are x=2(3+sqrt(3)),x=2(3-sqrt(3))
Find the zeros of x^2-12x=-24
The zeros of x^2-12x=-24 are x=2(3+sqrt(3)),x=2(3-sqrt(3))