What are the solutions to the equation x^2+13=8x+37 ?

The solutions to the equation x^2+13=8x+37 are x=2(2+sqrt(10)),x=2(2-sqrt(10))

Find the zeros of x^2+13=8x+37

The zeros of x^2+13=8x+37 are x=2(2+sqrt(10)),x=2(2-sqrt(10))

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x^{2} + 13 = 8 x + 37

x = 2 (2 + 10), x = 2 (2 - 10)

Decimal Notation

x = 10.32455 \dots, x = - 2.32455 \dots

Solution steps

x^{2} + 13 = 8 x + 37

Move

37

to the left side

x^{2} - 24 = 8 x

Move

8 x

to the left side

x^{2} - 24 - 8 x = 0

Write in the standard form

a x^{2} + b x + c = 0

x^{2} - 8 x - 24 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 8 ) \pm ( - 8 ) ^{2} - 4 \cdot 1 \cdot ( - 24 )}{2 \cdot 1}

(- 8)^{2} - 4 \cdot 1 \cdot (- 24) = 410

x_{1, 2} = \frac{- ( - 8 ) \pm 4 10}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 4 10}{2 \cdot 1}, x_{2} = \frac{- ( - 8 ) - 4 10}{2 \cdot 1}

x = \frac{- ( - 8 ) + 4 10}{2 \cdot 1} : 2 (2 + 10)

x = \frac{- ( - 8 ) - 4 10}{2 \cdot 1} : 2 (2 - 10)

The solutions to the quadratic equation are:

x = 2 (2 + 10), x = 2 (2 - 10)

x^{2} - 12 x + 36 = 44

(x + 8) (2 x - 10) = 0

x^{2} + 6 x - 9 = 0

(x - 2)^{2} = 12 (x - 2)

x^{2} + 15 x - 3 = 0

What are the solutions to the equation x^2+13=8x+37 ?
The solutions to the equation x^2+13=8x+37 are x=2(2+sqrt(10)),x=2(2-sqrt(10))
Find the zeros of x^2+13=8x+37
The zeros of x^2+13=8x+37 are x=2(2+sqrt(10)),x=2(2-sqrt(10))