Solve -2x^2-5x=2 - ScanMath

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}{2}

Alternative Form

x_{1} = - 2, x_{2} = - 0.5

Evaluate

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

Move the expression to the left side

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

Factor the expression

More Steps

Evaluate

- 2 x^{2} - 5 x - 2

Factor out - 1 from the expression

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

Factor the expression

More Steps

Evaluate

2 x^{2} + 5 x + 2

Rewrite the expression

2 x^{2} + (1 + 4) x + 2

Calculate

2 x^{2} + x + 4 x + 2

Rewrite the expression

x \times 2 x + x + 2 \times 2 x + 2

Factor out x from the expression

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

Factor out 2 from the expression

x (2 x + 1) + 2 (2 x + 1)

Factor out 2 x + 1 from the expression

(x + 2) (2 x + 1)

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

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

Divide the terms

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

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

2 x + 1 = 0 x + 2 = 0

Solve the equation for x

More Steps

Evaluate

2 x + 1 = 0

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

2 x = 0 - 1

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

2 x = - 1

Divide both sides

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

Divide the numbers

x = \frac{- 1}{2}

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

x = - \frac{1}{2}

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

Solution

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

Alternative Form

x_{1} = - 2, x_{2} = - 0.5

Show Solution