Solve -2x^2+3x+5=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

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

Alternative Form

x_{1} = - 1, x_{2} = 2.5

Evaluate

- 2 x^{2} + 3 x + 5 = 0

Factor the expression

More Steps

Evaluate

- 2 x^{2} + 3 x + 5

Rewrite the expression

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

Calculate

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

Rewrite the expression

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

Factor out - x from the expression

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

Factor out - 1 from the expression

- x (2 x - 5) - (2 x - 5)

Factor out 2 x - 5 from the expression

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

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

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

2 x - 5 = 0 - x - 1 = 0

Solve the equation for x

More Steps

Evaluate

2 x - 5 = 0

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

2 x = 0 + 5

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

2 x = 5

Divide both sides

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

Divide the numbers

x = \frac{5}{2}

x = \frac{5}{2} - 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

Change the signs on both sides of the equation

x = - 1

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

Solution

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

Alternative Form

x_{1} = - 1, x_{2} = 2.5

Show Solution