Solve 7911a^2-16 - ScanMath

Question

Find the roots

a_{1} = - \frac{4 879}{2637}, a_{2} = \frac{4 879}{2637}

Alternative Form

a_{1} \approx - 0.044972, a_{2} \approx 0.044972

Evaluate

7911 a^{2} - 16

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

7911 a^{2} - 16 = 0

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

7911 a^{2} = 0 + 16

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

7911 a^{2} = 16

Divide both sides

\frac{7911 a ^{2}}{7911} = \frac{16}{7911}

Divide the numbers

a^{2} = \frac{16}{7911}

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

a = \pm \frac{16}{7911}

Simplify the expression

More Steps

Evaluate

\frac{16}{7911}

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

\frac{16}{7911}

Simplify the radical expression

More Steps

Evaluate

16

Write the number in exponential form with the base of 4

4^{2}

Reduce the index of the radical and exponent with 2

4

\frac{4}{7911}

Simplify the radical expression

More Steps

Evaluate

7911

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

9 \times 879

Write the number in exponential form with the base of 3

3^{2} \times 879

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

3^{2} \times 879

Reduce the index of the radical and exponent with 2

3879

\frac{4}{3 879}

Multiply by the Conjugate

\frac{4 879}{3 879 \times 879}

Multiply the numbers

More Steps

Evaluate

3879 \times 879

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

3 \times 879

Multiply the terms

2637

\frac{4 879}{2637}

a = \pm \frac{4 879}{2637}

Separate the equation into 2 possible cases

a = \frac{4 879}{2637} a = - \frac{4 879}{2637}

Solution

a_{1} = - \frac{4 879}{2637}, a_{2} = \frac{4 879}{2637}

Alternative Form

a_{1} \approx - 0.044972, a_{2} \approx 0.044972

Show Solution