What are the solutions to the equation w^2-14w+2=-4w ?

The solutions to the equation w^2-14w+2=-4w are w=5+sqrt(23),w=5-sqrt(23)

Find the zeros of w^2-14w+2=-4w

The zeros of w^2-14w+2=-4w are w=5+sqrt(23),w=5-sqrt(23)

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w^{2} - 14 w + 2 = - 4 w

w = 5 + 23, w = 5 - 23

Decimal

w = 9.79583 \dots, w = 0.20416 \dots

Solution steps

w^{2} - 14 w + 2 = - 4 w

Move

4 w

to the left side

w^{2} - 10 w + 2 = 0

Solve with the quadratic formula

w_{1, 2} = \frac{- ( - 10 ) \pm ( - 10 ) ^{2} - 4 \cdot 1 \cdot 2}{2 \cdot 1}

(- 10)^{2} - 4 \cdot 1 \cdot 2 = 223

w_{1, 2} = \frac{- ( - 10 ) \pm 2 23}{2 \cdot 1}

Separate the solutions

w_{1} = \frac{- ( - 10 ) + 2 23}{2 \cdot 1}, w_{2} = \frac{- ( - 10 ) - 2 23}{2 \cdot 1}

w = \frac{- ( - 10 ) + 2 23}{2 \cdot 1} : 5 + 23

w = \frac{- ( - 10 ) - 2 23}{2 \cdot 1} : 5 - 23

The solutions to the quadratic equation are:

w = 5 + 23, w = 5 - 23

7 x^{2} + 8 x + 3 = 0

3 x^{2} - 9 x - 84 = 0

8 x^{2} = - 128

y, x^{2} + y^{2} - 5 = 2 x y + y^{2} - 5

0 = 6 x^{2} - 7 x + 2

What are the solutions to the equation w^2-14w+2=-4w ?
The solutions to the equation w^2-14w+2=-4w are w=5+sqrt(23),w=5-sqrt(23)
Find the zeros of w^2-14w+2=-4w
The zeros of w^2-14w+2=-4w are w=5+sqrt(23),w=5-sqrt(23)