Solve 13-2904a^2 - ScanMath

Question

Find the roots

a_{1} = - \frac{78}{132}, a_{2} = \frac{78}{132}

Alternative Form

a_{1} \approx - 0.066907, a_{2} \approx 0.066907

Evaluate

13 - 2904 a^{2}

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

13 - 2904 a^{2} = 0

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

- 2904 a^{2} = 0 - 13

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

- 2904 a^{2} = - 13

Change the signs on both sides of the equation

2904 a^{2} = 13

Divide both sides

\frac{2904 a ^{2}}{2904} = \frac{13}{2904}

Divide the numbers

a^{2} = \frac{13}{2904}

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

a = \pm \frac{13}{2904}

Simplify the expression

More Steps

Evaluate

\frac{13}{2904}

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

\frac{13}{2904}

Simplify the radical expression

More Steps

Evaluate

2904

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

484 \times 6

Write the number in exponential form with the base of 22

2 2^{2} \times 6

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

2 2^{2} \times 6

Reduce the index of the radical and exponent with 2

226

\frac{13}{22 6}

Multiply by the Conjugate

\frac{13 \times 6}{22 6 \times 6}

Multiply the numbers

More Steps

Evaluate

13 \times 6

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

13 \times 6

Calculate the product

78

\frac{78}{22 6 \times 6}

Multiply the numbers

More Steps

Evaluate

226 \times 6

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

22 \times 6

Multiply the terms

132

\frac{78}{132}

a = \pm \frac{78}{132}

Separate the equation into 2 possible cases

a = \frac{78}{132} a = - \frac{78}{132}

Solution

a_{1} = - \frac{78}{132}, a_{2} = \frac{78}{132}

Alternative Form

a_{1} \approx - 0.066907, a_{2} \approx 0.066907

Show Solution