Solve 8d^2-15 - ScanMath

Question

Find the roots

d_{1} = - \frac{30}{4}, d_{2} = \frac{30}{4}

Alternative Form

d_{1} \approx - 1.369306, d_{2} \approx 1.369306

Evaluate

8 d^{2} - 15

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

8 d^{2} - 15 = 0

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

8 d^{2} = 0 + 15

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

8 d^{2} = 15

Divide both sides

\frac{8 d ^{2}}{8} = \frac{15}{8}

Divide the numbers

d^{2} = \frac{15}{8}

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

d = \pm \frac{15}{8}

Simplify the expression

More Steps

Evaluate

\frac{15}{8}

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

\frac{15}{8}

Simplify the radical expression

More Steps

Evaluate

8

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 2

Write the number in exponential form with the base of 2

2^{2} \times 2

The root of a product is equal to the product of the roots of each factor

2^{2} \times 2

Reduce the index of the radical and exponent with 2

22

\frac{15}{2 2}

Multiply by the Conjugate

\frac{15 \times 2}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

15 \times 2

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

15 \times 2

Calculate the product

30

\frac{30}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

22 \times 2

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

2 \times 2

Multiply the numbers

4

\frac{30}{4}

d = \pm \frac{30}{4}

Separate the equation into 2 possible cases

d = \frac{30}{4} d = - \frac{30}{4}

Solution

d_{1} = - \frac{30}{4}, d_{2} = \frac{30}{4}

Alternative Form

d_{1} \approx - 1.369306, d_{2} \approx 1.369306

Show Solution