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

Question

Simplify the expression

4 x^{2} - 25

Evaluate

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

Use (a + b) (a - b) = a^{2} - b^{2} to simplify the product

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

Evaluate the power

More Steps

Evaluate

(2 x)^{2}

To raise a product to a power,raise each factor to that power

2^{2} x^{2}

Evaluate the power

4 x^{2}

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

Solution

4 x^{2} - 25

Show Solution

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

Alternative Form

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

Evaluate

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

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

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

Separate the equation into 2 possible cases

2 x + 5 = 0 2 x - 5 = 0

Solve the equation

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}

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

x = - \frac{5}{2}

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

Solve the equation

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 = \frac{5}{2}

Solution

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

Alternative Form

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

Show Solution