Solve 9z^2-18z=1 - ScanMath

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

z_{1} = \frac{3 - 10}{3}, z_{2} = \frac{3 + 10}{3}

Alternative Form

z_{1} \approx - 0.054093, z_{2} \approx 2.054093

Evaluate

9 z^{2} - 18 z = 1

Move the expression to the left side

9 z^{2} - 18 z - 1 = 0

Substitute a= 9,b= - 18 and c= - 1 into the quadratic formula z = \frac{- b \pm b ^{2} - 4 a c}{2 a}

z = \frac{18 \pm ( - 18 ) ^{2} - 4 \times 9 ( - 1 )}{2 \times 9}

Simplify the expression

z = \frac{18 \pm ( - 18 ) ^{2} - 4 \times 9 ( - 1 )}{18}

Simplify the expression

More Steps

z = \frac{18 \pm 360}{18}

Simplify the radical expression

More Steps

z = \frac{18 \pm 6 10}{18}

Separate the equation into 2 possible cases

z = \frac{18 + 6 10}{18} z = \frac{18 - 6 10}{18}

Simplify the expression

More Steps

z = \frac{3 + 10}{3} z = \frac{18 - 6 10}{18}

Simplify the expression

More Steps

z = \frac{3 + 10}{3} z = \frac{3 - 10}{3}

Solution

z_{1} = \frac{3 - 10}{3}, z_{2} = \frac{3 + 10}{3}

Alternative Form

z_{1} \approx - 0.054093, z_{2} \approx 2.054093

Show Solution