Solve 10000x^(2)-64

Question

Factor the expression

16 (25 x - 2) (25 x + 2)

Evaluate

10000 x^{2} - 64

Factor out 16 from the expression

16 (625 x^{2} - 4)

Solution

More Steps

Evaluate

625 x^{2} - 4

Rewrite the expression in exponential form

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

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(25 x - 2) (25 x + 2)

16 (25 x - 2) (25 x + 2)

Show Solution

x_{1} = - \frac{2}{25}, x_{2} = \frac{2}{25}

Alternative Form

x_{1} = - 0.08, x_{2} = 0.08

Evaluate

10000 x^{2} - 64

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

10000 x^{2} - 64 = 0

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

10000 x^{2} = 0 + 64

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

10000 x^{2} = 64

Divide both sides

\frac{10000 x ^{2}}{10000} = \frac{64}{10000}

Divide the numbers

x^{2} = \frac{64}{10000}

Cancel out the common factor 16

x^{2} = \frac{4}{625}

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

x = \pm \frac{4}{625}

Simplify the expression

More Steps

Evaluate

\frac{4}{625}

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

\frac{4}{625}

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{2}{625}

Simplify the radical expression

More Steps

Evaluate

625

Write the number in exponential form with the base of 25

2 5^{2}

Reduce the index of the radical and exponent with 2

25

\frac{2}{25}

x = \pm \frac{2}{25}

Separate the equation into 2 possible cases

x = \frac{2}{25} x = - \frac{2}{25}

Solution

x_{1} = - \frac{2}{25}, x_{2} = \frac{2}{25}

Alternative Form

x_{1} = - 0.08, x_{2} = 0.08

Show Solution