Solve 128 - 50x^2

Question

Factor the expression

2 (8 - 5 x) (8 + 5 x)

Evaluate

128 - 50 x^{2}

Factor out 2 from the expression

2 (64 - 25 x^{2})

Solution

More Steps

Evaluate

64 - 25 x^{2}

Rewrite the expression in exponential form

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

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

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

2 (8 - 5 x) (8 + 5 x)

Show Solution

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

Alternative Form

x_{1} = - 1.6, x_{2} = 1.6

Evaluate

128 - 50 x^{2}

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

128 - 50 x^{2} = 0

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

- 50 x^{2} = 0 - 128

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

- 50 x^{2} = - 128

Change the signs on both sides of the equation

50 x^{2} = 128

Divide both sides

\frac{50 x ^{2}}{50} = \frac{128}{50}

Divide the numbers

x^{2} = \frac{128}{50}

Cancel out the common factor 2

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

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

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

Simplify the expression

More Steps

Evaluate

\frac{64}{25}

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

\frac{64}{25}

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{8}{25}

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{8}{5}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

x_{1} = - 1.6, x_{2} = 1.6

Show Solution