Solve 8k^2 - 50 - ScanMath

Question

Factor the expression

2 (2 k - 5) (2 k + 5)

Evaluate

8 k^{2} - 50

Factor out 2 from the expression

2 (4 k^{2} - 25)

Solution

More Steps

Evaluate

4 k^{2} - 25

Rewrite the expression in exponential form

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

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

(2 k - 5) (2 k + 5)

2 (2 k - 5) (2 k + 5)

Show Solution

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

Alternative Form

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

Evaluate

8 k^{2} - 50

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

8 k^{2} - 50 = 0

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

8 k^{2} = 0 + 50

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

8 k^{2} = 50

Divide both sides

\frac{8 k ^{2}}{8} = \frac{50}{8}

Divide the numbers

k^{2} = \frac{50}{8}

Cancel out the common factor 2

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

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

k = \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}

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

Separate the equation into 2 possible cases

k = \frac{5}{2} k = - \frac{5}{2}

Solution

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

Alternative Form

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

Show Solution