Solve 64x^2-25 - ScanMath

Question

Factor the expression

(8 x - 5) (8 x + 5)

Evaluate

64 x^{2} - 25

Rewrite the expression in exponential form

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

Solution

(8 x - 5) (8 x + 5)

Show Solution

x_{1} = - \frac{5}{8}, x_{2} = \frac{5}{8}

Alternative Form

x_{1} = - 0.625, x_{2} = 0.625

Evaluate

64 x^{2} - 25

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

64 x^{2} - 25 = 0

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

64 x^{2} = 0 + 25

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

64 x^{2} = 25

Divide both sides

\frac{64 x ^{2}}{64} = \frac{25}{64}

Divide the numbers

x^{2} = \frac{25}{64}

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

x = \pm \frac{25}{64}

Simplify the expression

More Steps

Evaluate

\frac{25}{64}

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

\frac{25}{64}

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}{64}

Simplify the radical expression

More Steps

Evaluate

64

Write the number in exponential form with the base of 8

8^{2}

Reduce the index of the radical and exponent with 2

8

\frac{5}{8}

x = \pm \frac{5}{8}

Separate the equation into 2 possible cases

x = \frac{5}{8} x = - \frac{5}{8}

Solution

x_{1} = - \frac{5}{8}, x_{2} = \frac{5}{8}

Alternative Form

x_{1} = - 0.625, x_{2} = 0.625

Show Solution