Solve 9x^2-18x=7 - ScanMath

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{1}{3}, x_{2} = \frac{7}{3}

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 2. \dot{3}

Evaluate

9 x^{2} - 18 x = 7

Move the expression to the left side

9 x^{2} - 18 x - 7 = 0

Factor the expression

More Steps

Evaluate

9 x^{2} - 18 x - 7

Rewrite the expression

9 x^{2} + (3 - 21) x - 7

Calculate

9 x^{2} + 3 x - 21 x - 7

Rewrite the expression

3 x \times 3 x + 3 x - 7 \times 3 x - 7

Factor out 3 x from the expression

3 x (3 x + 1) - 7 \times 3 x - 7

Factor out - 7 from the expression

3 x (3 x + 1) - 7 (3 x + 1)

Factor out 3 x + 1 from the expression

(3 x - 7) (3 x + 1)

(3 x - 7) (3 x + 1) = 0

When the product of factors equals 0,at least one factor is 0

3 x - 7 = 0 3 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 7 = 0

Move the constant to the right-hand side and change its sign

3 x = 0 + 7

Removing 0 doesn't change the value,so remove it from the expression

3 x = 7

Divide both sides

\frac{3 x}{3} = \frac{7}{3}

Divide the numbers

x = \frac{7}{3}

x = \frac{7}{3} 3 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

3 x + 1 = 0

Move the constant to the right-hand side and change its sign

3 x = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

3 x = - 1

Divide both sides

\frac{3 x}{3} = \frac{- 1}{3}

Divide the numbers

x = \frac{- 1}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{1}{3}

x = \frac{7}{3} x = - \frac{1}{3}

Solution

x_{1} = - \frac{1}{3}, x_{2} = \frac{7}{3}

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 2. \dot{3}

Show Solution