What are the solutions to the equation x^2= 1/2 (30-x)^2 ?

The solutions to the equation x^2= 1/2 (30-x)^2 are x=-30(1+sqrt(2)),x=30(sqrt(2)-1)

Find the zeros of x^2= 1/2 (30-x)^2

The zeros of x^2= 1/2 (30-x)^2 are x=-30(1+sqrt(2)),x=30(sqrt(2)-1)

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x^{2} = \frac{1}{2} (30 - x)^{2}

x = - 30 (1 + 2), x = 30 (2 - 1)

Decimal Notation

x = - 72.42640 \dots, x = 12.42640 \dots

Solution steps

x^{2} = \frac{1}{2} (30 - x)^{2}

Multiply both sides by

2

2 x^{2} = (30 - x)^{2}

Expand

(30 - x)^{2} : 900 - 60 x + x^{2}

2 x^{2} = 900 - 60 x + x^{2}

Switch sides

900 - 60 x + x^{2} = 2 x^{2}

Move

2 x^{2}

to the left side

900 - 60 x - x^{2} = 0

Write in the standard form

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

- x^{2} - 60 x + 900 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 60 ) \pm ( - 60 ) ^{2} - 4 ( - 1 ) \cdot 900}{2 ( - 1 )}

(- 60)^{2} - 4 (- 1) \cdot 900 = 602

x_{1, 2} = \frac{- ( - 60 ) \pm 60 2}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- ( - 60 ) + 60 2}{2 ( - 1 )}, x_{2} = \frac{- ( - 60 ) - 60 2}{2 ( - 1 )}

x = \frac{- ( - 60 ) + 60 2}{2 ( - 1 )} : - 30 (1 + 2)

x = \frac{- ( - 60 ) - 60 2}{2 ( - 1 )} : 30 (2 - 1)

The solutions to the quadratic equation are:

x = - 30 (1 + 2), x = 30 (2 - 1)

5 n^{2} - 20 n + 6 = 0

x^{2} + 5 x - 7

x^{2} + 5 x - 1

x^{2} + 5 x - 3

3 x - 7 + x (x - 3) = 2 x + 8

What are the solutions to the equation x^2= 1/2 (30-x)^2 ?
The solutions to the equation x^2= 1/2 (30-x)^2 are x=-30(1+sqrt(2)),x=30(sqrt(2)-1)
Find the zeros of x^2= 1/2 (30-x)^2
The zeros of x^2= 1/2 (30-x)^2 are x=-30(1+sqrt(2)),x=30(sqrt(2)-1)