What are the solutions to the equation -5z^2-10z+1=-6z^2 ?

The solutions to the equation -5z^2-10z+1=-6z^2 are z=5+2sqrt(6),z=5-2sqrt(6)

Find the zeros of -5z^2-10z+1=-6z^2

The zeros of -5z^2-10z+1=-6z^2 are z=5+2sqrt(6),z=5-2sqrt(6)

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- 5 z^{2} - 10 z + 1 = - 6 z^{2}

z = 5 + 26, z = 5 - 26

Decimal Notation

z = 9.89897 \dots, z = 0.10102 \dots

Solution steps

- 5 z^{2} - 10 z + 1 = - 6 z^{2}

Move

6 z^{2}

to the left side

z^{2} - 10 z + 1 = 0

Solve with the quadratic formula

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

(- 10)^{2} - 4 \cdot 1 \cdot 1 = 46

z_{1, 2} = \frac{- ( - 10 ) \pm 4 6}{2 \cdot 1}

Separate the solutions

z_{1} = \frac{- ( - 10 ) + 4 6}{2 \cdot 1}, z_{2} = \frac{- ( - 10 ) - 4 6}{2 \cdot 1}

z = \frac{- ( - 10 ) + 4 6}{2 \cdot 1} : 5 + 26

z = \frac{- ( - 10 ) - 4 6}{2 \cdot 1} : 5 - 26

The solutions to the quadratic equation are:

z = 5 + 26, z = 5 - 26

6 x + 3 = 2 x^{2}

x^{2} - \frac{4}{5} x - 1

z^{2} - 2 z

z^{2} + 3 z - 7 = z

x^{2} + 2 x - 8 = 0

What are the solutions to the equation -5z^2-10z+1=-6z^2 ?
The solutions to the equation -5z^2-10z+1=-6z^2 are z=5+2sqrt(6),z=5-2sqrt(6)
Find the zeros of -5z^2-10z+1=-6z^2
The zeros of -5z^2-10z+1=-6z^2 are z=5+2sqrt(6),z=5-2sqrt(6)