Solve 6x^2 -8=5x-7

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{1}{6}, x_{2} = 1

Alternative Form

x_{1} = - 0.1 \dot{6}, x_{2} = 1

Evaluate

6 x^{2} - 8 = 5 x - 7

Move the expression to the left side

6 x^{2} - 1 - 5 x = 0

Factor the expression

More Steps

Evaluate

6 x^{2} - 1 - 5 x

Reorder the terms

6 x^{2} - 5 x - 1

Rewrite the expression

6 x^{2} + (1 - 6) x - 1

Calculate

6 x^{2} + x - 6 x - 1

Rewrite the expression

x \times 6 x + x - 6 x - 1

Factor out x from the expression

x (6 x + 1) - 6 x - 1

Factor out - 1 from the expression

x (6 x + 1) - (6 x + 1)

Factor out 6 x + 1 from the expression

(x - 1) (6 x + 1)

(x - 1) (6 x + 1) = 0

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

x - 1 = 0 6 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 1 6 x + 1 = 0

Solve the equation for x

More Steps

Evaluate

6 x + 1 = 0

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

6 x = 0 - 1

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

6 x = - 1

Divide both sides

\frac{6 x}{6} = \frac{- 1}{6}

Divide the numbers

x = \frac{- 1}{6}

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

x = - \frac{1}{6}

x = 1 x = - \frac{1}{6}

Solution

x_{1} = - \frac{1}{6}, x_{2} = 1

Alternative Form

x_{1} = - 0.1 \dot{6}, x_{2} = 1

Show Solution