Solve 2x-5x^2+7=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{7}{5}

Alternative Form

x_{1} = - 1, x_{2} = 1.4

Evaluate

2 x - 5 x^{2} + 7 = 0

Factor the expression

More Steps

Evaluate

2 x - 5 x^{2} + 7

Reorder the terms

- 5 x^{2} + 2 x + 7

Rewrite the expression

- 5 x^{2} + (7 - 5) x + 7

Calculate

- 5 x^{2} + 7 x - 5 x + 7

Rewrite the expression

- x \times 5 x + x \times 7 - 5 x + 7

Factor out - x from the expression

- x (5 x - 7) - 5 x + 7

Factor out - 1 from the expression

- x (5 x - 7) - (5 x - 7)

Factor out 5 x - 7 from the expression

(- x - 1) (5 x - 7)

(- x - 1) (5 x - 7) = 0

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

5 x - 7 = 0 - x - 1 = 0

Solve the equation for x

More Steps

Evaluate

5 x - 7 = 0

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

5 x = 0 + 7

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

5 x = 7

Divide both sides

\frac{5 x}{5} = \frac{7}{5}

Divide the numbers

x = \frac{7}{5}

x = \frac{7}{5} - 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{7}{5} x = - 1

Solution

x_{1} = - 1, x_{2} = \frac{7}{5}

Alternative Form

x_{1} = - 1, x_{2} = 1.4

Show Solution