Solve 4+7x-2x^2=0

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve by completing the square

x_{1} = - \frac{1}{2}, x_{2} = 4

Alternative Form

x_{1} = - 0.5, x_{2} = 4

Evaluate

4 + 7 x - 2 x^{2} = 0

Factor the expression

More Steps

Evaluate

4 + 7 x - 2 x^{2}

Rewrite the expression

4 + (8 - 1) x - 2 x^{2}

Calculate

4 + 8 x - x - 2 x^{2}

Rewrite the expression

4 + 4 \times 2 x - x - x \times 2 x

Factor out 4 from the expression

4 (1 + 2 x) - x - x \times 2 x

Factor out - x from the expression

4 (1 + 2 x) - x (1 + 2 x)

Factor out 1 + 2 x from the expression

(4 - x) (1 + 2 x)

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

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

4 - x = 0 1 + 2 x = 0

Solve the equation for x

More Steps

Evaluate

4 - x = 0

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

- x = 0 - 4

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

- x = - 4

Change the signs on both sides of the equation

x = 4

x = 4 1 + 2 x = 0

Solve the equation for x

More Steps

Evaluate

1 + 2 x = 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 = 4 x = - \frac{1}{2}

Solution

x_{1} = - \frac{1}{2}, x_{2} = 4

Alternative Form

x_{1} = - 0.5, x_{2} = 4

Show Solution