Solve 3(3b^2 -35)

Question

Simplify the expression

9 b^{2} - 105

Evaluate

3 (3 b^{2} - 35)

Apply the distributive property

3 \times 3 b^{2} - 3 \times 35

Multiply the numbers

9 b^{2} - 3 \times 35

Solution

9 b^{2} - 105

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

3 (3 b^{2} - 35)

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

3 (3 b^{2} - 35) = 0

Rewrite the expression

3 b^{2} - 35 = 0

Move the constant to the right side

3 b^{2} = 35

Divide both sides

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

Divide the numbers

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