Solve 4x^2-8x-5 - ScanMath

Question

Factor the expression

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

Evaluate

4 x^{2} - 8 x - 5

Rewrite the expression

4 x^{2} + (2 - 10) x - 5

Calculate

4 x^{2} + 2 x - 10 x - 5

Rewrite the expression

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

Factor out 2 x from the expression

2 x (2 x + 1) - 5 \times 2 x - 5

Factor out - 5 from the expression

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

Solution

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

Show Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 2.5

Evaluate

4 x^{2} - 8 x - 5

To find the roots of the expression,set the expression equal to 0

4 x^{2} - 8 x - 5 = 0

Factor the expression

More Steps

Evaluate

4 x^{2} - 8 x - 5

Rewrite the expression

4 x^{2} + (2 - 10) x - 5

Calculate

4 x^{2} + 2 x - 10 x - 5

Rewrite the expression

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

Factor out 2 x from the expression

2 x (2 x + 1) - 5 \times 2 x - 5

Factor out - 5 from the expression

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

Factor out 2 x + 1 from the expression

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

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

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

2 x - 5 = 0 2 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} 2 x + 1 = 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{5}{2} x = - \frac{1}{2}

Solution

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

Alternative Form

x_{1} = - 0.5, x_{2} = 2.5

Show Solution