Solve 9b^2 -105 - ScanMath

Question

Factor the expression

3 (3 b^{2} - 35)

Evaluate

9 b^{2} - 105

Solution

3 (3 b^{2} - 35)

Show Solution

b_{1} = - \frac{105}{3}, b_{2} = \frac{105}{3}

Alternative Form

b_{1} \approx - 3.41565, b_{2} \approx 3.41565

Evaluate

9 b^{2} - 105

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

9 b^{2} - 105 = 0

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

9 b^{2} = 0 + 105

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

9 b^{2} = 105

Divide both sides

\frac{9 b ^{2}}{9} = \frac{105}{9}

Divide the numbers

b^{2} = \frac{105}{9}

Cancel out the common factor 3

b^{2} = \frac{35}{3}

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

b = \pm \frac{35}{3}

Simplify the expression

More Steps

Evaluate

\frac{35}{3}

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

\frac{35}{3}

Multiply by the Conjugate

\frac{35 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

35 \times 3

The product of roots with the same index is equal to the root of the product

35 \times 3

Calculate the product

105

\frac{105}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{105}{3}

b = \pm \frac{105}{3}

Separate the equation into 2 possible cases

b = \frac{105}{3} b = - \frac{105}{3}

Solution

b_{1} = - \frac{105}{3}, b_{2} = \frac{105}{3}

Alternative Form

b_{1} \approx - 3.41565, b_{2} \approx 3.41565

Show Solution