What are the solutions to the equation x^2+(12-x)^2=74 ?

The solutions to the equation x^2+(12-x)^2=74 are x=7,x=5

Find the zeros of x^2+(12-x)^2=74

The zeros of x^2+(12-x)^2=74 are x=7,x=5

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x^{2} + (12 - x)^{2} = 74

x = 7, x = 5

Solution steps

x^{2} + (12 - x)^{2} = 74

Expand

x^{2} + (12 - x)^{2} : 2 x^{2} - 24 x + 144

2 x^{2} - 24 x + 144 = 74

Move

74

to the left side

2 x^{2} - 24 x + 70 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 24 ) \pm ( - 24 ) ^{2} - 4 \cdot 2 \cdot 70}{2 \cdot 2}

(- 24)^{2} - 4 \cdot 2 \cdot 70 = 4

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

Separate the solutions

x_{1} = \frac{- ( - 24 ) + 4}{2 \cdot 2}, x_{2} = \frac{- ( - 24 ) - 4}{2 \cdot 2}

x = \frac{- ( - 24 ) + 4}{2 \cdot 2} : 7

x = \frac{- ( - 24 ) - 4}{2 \cdot 2} : 5

The solutions to the quadratic equation are:

x = 7, x = 5

(x + 1)^{2} < 0

2 x^{2} - 2 x \geq 4

4 (x + 2)^{2} - 5 (x + 2) + 1

- \frac{3}{2} = - \frac{3}{2} x

16 t^{2} = 0

What are the solutions to the equation x^2+(12-x)^2=74 ?
The solutions to the equation x^2+(12-x)^2=74 are x=7,x=5
Find the zeros of x^2+(12-x)^2=74
The zeros of x^2+(12-x)^2=74 are x=7,x=5