Solve 4x^2 - 25 - ScanMath

Question

Factor the expression

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

Evaluate

4 x^{2} - 25

Rewrite the expression in exponential form

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

Solution

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

Show Solution

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

Alternative Form

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

Evaluate

4 x^{2} - 25

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

4 x^{2} - 25 = 0

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

4 x^{2} = 0 + 25

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

4 x^{2} = 25

Divide both sides

\frac{4 x ^{2}}{4} = \frac{25}{4}

Divide the numbers

x^{2} = \frac{25}{4}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{25}{4}

Simplify the expression

More Steps

Evaluate

\frac{25}{4}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{25}{4}

Simplify the radical expression

More Steps

Evaluate

25

Write the number in exponential form with the base of 5

5^{2}

Reduce the index of the radical and exponent with 2

5

\frac{5}{4}

Simplify the radical expression

More Steps

Evaluate

4

Write the number in exponential form with the base of 2

2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{5}{2}

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

Separate the equation into 2 possible cases

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