Solve -10x^2-27=33x

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{9}{5}, x_{2} = - \frac{3}{2}

Alternative Form

x_{1} = - 1.8, x_{2} = - 1.5

Evaluate

- 10 x^{2} - 27 = 33 x

Move the expression to the left side

- 10 x^{2} - 27 - 33 x = 0

Factor the expression

More Steps

Evaluate

- 10 x^{2} - 27 - 33 x

Evaluate

- 10 x^{2} - 33 x - 27

Factor out - 1 from the expression

- (10 x^{2} + 33 x + 27)

Factor the expression

More Steps

Evaluate

10 x^{2} + 33 x + 27

Rewrite the expression

10 x^{2} + (18 + 15) x + 27

Calculate

10 x^{2} + 18 x + 15 x + 27

Rewrite the expression

2 x \times 5 x + 2 x \times 9 + 3 \times 5 x + 3 \times 9

Factor out 2 x from the expression

2 x (5 x + 9) + 3 \times 5 x + 3 \times 9

Factor out 3 from the expression

2 x (5 x + 9) + 3 (5 x + 9)

Factor out 5 x + 9 from the expression

(2 x + 3) (5 x + 9)

- (2 x + 3) (5 x + 9)

- (2 x + 3) (5 x + 9) = 0

Divide the terms

(2 x + 3) (5 x + 9) = 0

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

2 x + 3 = 0 5 x + 9 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 3 = 0

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

2 x = 0 - 3

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

2 x = - 3

Divide both sides

\frac{2 x}{2} = \frac{- 3}{2}

Divide the numbers

x = \frac{- 3}{2}

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

x = - \frac{3}{2}

x = - \frac{3}{2} 5 x + 9 = 0

Solve the equation for x

More Steps

Evaluate

5 x + 9 = 0

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

5 x = 0 - 9

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

5 x = - 9

Divide both sides

\frac{5 x}{5} = \frac{- 9}{5}

Divide the numbers

x = \frac{- 9}{5}

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

x = - \frac{9}{5}

x = - \frac{3}{2} x = - \frac{9}{5}

Solution

x_{1} = - \frac{9}{5}, x_{2} = - \frac{3}{2}

Alternative Form

x_{1} = - 1.8, x_{2} = - 1.5

Show Solution