Solve 69474a^2-5 - ScanMath

Question

Find the roots

a_{1} = - \frac{347370}{69474}, a_{2} = \frac{347370}{69474}

Alternative Form

a_{1} \approx - 0.008483, a_{2} \approx 0.008483

Evaluate

69474 a^{2} - 5

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

69474 a^{2} - 5 = 0

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

69474 a^{2} = 0 + 5

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

69474 a^{2} = 5

Divide both sides

\frac{69474 a ^{2}}{69474} = \frac{5}{69474}

Divide the numbers

a^{2} = \frac{5}{69474}

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

a = \pm \frac{5}{69474}

Simplify the expression

More Steps

Evaluate

\frac{5}{69474}

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

\frac{5}{69474}

Multiply by the Conjugate

\frac{5 \times 69474}{69474 \times 69474}

Multiply the numbers

More Steps

Evaluate

5 \times 69474

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

5 \times 69474

Calculate the product

347370

\frac{347370}{69474 \times 69474}

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

\frac{347370}{69474}

a = \pm \frac{347370}{69474}

Separate the equation into 2 possible cases

a = \frac{347370}{69474} a = - \frac{347370}{69474}

Solution

a_{1} = - \frac{347370}{69474}, a_{2} = \frac{347370}{69474}

Alternative Form

a_{1} \approx - 0.008483, a_{2} \approx 0.008483

Show Solution