Solve 5x^(2)-2=-9x

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - 2, x_{2} = \frac{1}{5}

Alternative Form

x_{1} = - 2, x_{2} = 0.2

Evaluate

5 x^{2} - 2 = - 9 x

Move the expression to the left side

5 x^{2} - 2 + 9 x = 0

Factor the expression

More Steps

Evaluate

5 x^{2} - 2 + 9 x

Reorder the terms

5 x^{2} + 9 x - 2

Rewrite the expression

5 x^{2} + (- 1 + 10) x - 2

Calculate

5 x^{2} - x + 10 x - 2

Rewrite the expression

x \times 5 x - x + 2 \times 5 x - 2

Factor out x from the expression

x (5 x - 1) + 2 \times 5 x - 2

Factor out 2 from the expression

x (5 x - 1) + 2 (5 x - 1)

Factor out 5 x - 1 from the expression

(x + 2) (5 x - 1)

(x + 2) (5 x - 1) = 0

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

5 x - 1 = 0 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

5 x - 1 = 0

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

5 x = 0 + 1

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

5 x = 1

Divide both sides

\frac{5 x}{5} = \frac{1}{5}

Divide the numbers

x = \frac{1}{5}

x = \frac{1}{5} x + 2 = 0

Solve the equation for x

More Steps

Evaluate

x + 2 = 0

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

x = 0 - 2

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

x = - 2

x = \frac{1}{5} x = - 2

Solution

x_{1} = - 2, x_{2} = \frac{1}{5}

Alternative Form

x_{1} = - 2, x_{2} = 0.2

Show Solution