What are the solutions to the equation (y-15)^2=40(y+35) ?

The solutions to the equation (y-15)^2=40(y+35) are y=5(7+4sqrt(6)),y=5(7-4sqrt(6))

Find the zeros of (y-15)^2=40(y+35)

The zeros of (y-15)^2=40(y+35) are y=5(7+4sqrt(6)),y=5(7-4sqrt(6))

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(y - 15)^{2} = 40 (y + 35)

y = 5 (7 + 46), y = 5 (7 - 46)

Decimal

y = 83.98979 \dots, y = - 13.98979 \dots

Solution steps

(y - 15)^{2} = 40 (y + 35)

Expand

(y - 15)^{2} : y^{2} - 30 y + 225

Expand

40 (y + 35) : 40 y + 1400

y^{2} - 30 y + 225 = 40 y + 1400

Move

1400

to the left side

y^{2} - 30 y - 1175 = 40 y

Move

40 y

to the left side

y^{2} - 70 y - 1175 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 70 ) \pm ( - 70 ) ^{2} - 4 \cdot 1 \cdot ( - 1175 )}{2 \cdot 1}

(- 70)^{2} - 4 \cdot 1 \cdot (- 1175) = 406

y_{1, 2} = \frac{- ( - 70 ) \pm 40 6}{2 \cdot 1}

Separate the solutions

y_{1} = \frac{- ( - 70 ) + 40 6}{2 \cdot 1}, y_{2} = \frac{- ( - 70 ) - 40 6}{2 \cdot 1}

y = \frac{- ( - 70 ) + 40 6}{2 \cdot 1} : 5 (7 + 46)

y = \frac{- ( - 70 ) - 40 6}{2 \cdot 1} : 5 (7 - 46)

The solutions to the quadratic equation are:

y = 5 (7 + 46), y = 5 (7 - 46)

x^{2} + 5 x + 6

25 (5 - 4 x)^{2} - 15 = - 14

y, x^{2} + 4 x y + y^{2} = 1

x^{2} + 53 = 14 x

27 x^{2} - 36 x - 37 = 0

What are the solutions to the equation (y-15)^2=40(y+35) ?
The solutions to the equation (y-15)^2=40(y+35) are y=5(7+4sqrt(6)),y=5(7-4sqrt(6))
Find the zeros of (y-15)^2=40(y+35)
The zeros of (y-15)^2=40(y+35) are y=5(7+4sqrt(6)),y=5(7-4sqrt(6))