Solve 16b^2-100 - ScanMath

Question

Factor the expression

4 (2 b - 5) (2 b + 5)

Evaluate

16 b^{2} - 100

Factor out 4 from the expression

4 (4 b^{2} - 25)

Solution

More Steps

Evaluate

4 b^{2} - 25

Rewrite the expression in exponential form

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

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

(2 b - 5) (2 b + 5)

4 (2 b - 5) (2 b + 5)

Show Solution

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

Alternative Form

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

Evaluate

16 b^{2} - 100

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

16 b^{2} - 100 = 0

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

16 b^{2} = 0 + 100

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

16 b^{2} = 100

Divide both sides

\frac{16 b ^{2}}{16} = \frac{100}{16}

Divide the numbers

b^{2} = \frac{100}{16}

Cancel out the common factor 4

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

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

b = \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}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

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

Show Solution