What are the solutions to the equation y^2-12y=-31 ?

The solutions to the equation y^2-12y=-31 are y=6+sqrt(5),y=6-sqrt(5)

Find the zeros of y^2-12y=-31

The zeros of y^2-12y=-31 are y=6+sqrt(5),y=6-sqrt(5)

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y^{2} - 12 y = - 31

y = 6 + 5, y = 6 - 5

Decimal Notation

y = 8.23606 \dots, y = 3.76393 \dots

Solution steps

y^{2} - 12 y = - 31

Move

31

to the left side

y^{2} - 12 y + 31 = 0

Solve with the quadratic formula

y_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 1 \cdot 31}{2 \cdot 1}

(- 12)^{2} - 4 \cdot 1 \cdot 31 = 25

y_{1, 2} = \frac{- ( - 12 ) \pm 2 5}{2 \cdot 1}

Separate the solutions

y_{1} = \frac{- ( - 12 ) + 2 5}{2 \cdot 1}, y_{2} = \frac{- ( - 12 ) - 2 5}{2 \cdot 1}

y = \frac{- ( - 12 ) + 2 5}{2 \cdot 1} : 6 + 5

y = \frac{- ( - 12 ) - 2 5}{2 \cdot 1} : 6 - 5

The solutions to the quadratic equation are:

y = 6 + 5, y = 6 - 5

7 - (2 x + 9) = 11 x - 5 (1 - x)

5 + 6

24 y^{2} - 80 y + 56

4 x^{2} y^{2} + 12 x y + 9

184

What are the solutions to the equation y^2-12y=-31 ?
The solutions to the equation y^2-12y=-31 are y=6+sqrt(5),y=6-sqrt(5)
Find the zeros of y^2-12y=-31
The zeros of y^2-12y=-31 are y=6+sqrt(5),y=6-sqrt(5)