Solve 5058-7a^2 - ScanMath

Question

Find the roots

a_{1} = - \frac{3 3934}{7}, a_{2} = \frac{3 3934}{7}

Alternative Form

a_{1} \approx - 26.880689, a_{2} \approx 26.880689

Evaluate

5058 - 7 a^{2}

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

5058 - 7 a^{2} = 0

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

- 7 a^{2} = 0 - 5058

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

- 7 a^{2} = - 5058

Change the signs on both sides of the equation

7 a^{2} = 5058

Divide both sides

\frac{7 a ^{2}}{7} = \frac{5058}{7}

Divide the numbers

a^{2} = \frac{5058}{7}

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

a = \pm \frac{5058}{7}

Simplify the expression

More Steps

Evaluate

\frac{5058}{7}

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

\frac{5058}{7}

Simplify the radical expression

More Steps

Evaluate

5058

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

9 \times 562

Write the number in exponential form with the base of 3

3^{2} \times 562

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

3^{2} \times 562

Reduce the index of the radical and exponent with 2

3562

\frac{3 562}{7}

Multiply by the Conjugate

\frac{3 562 \times 7}{7 \times 7}

Multiply the numbers

More Steps

Evaluate

562 \times 7

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

562 \times 7

Calculate the product

3934

\frac{3 3934}{7 \times 7}

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

\frac{3 3934}{7}

a = \pm \frac{3 3934}{7}

Separate the equation into 2 possible cases

a = \frac{3 3934}{7} a = - \frac{3 3934}{7}

Solution

a_{1} = - \frac{3 3934}{7}, a_{2} = \frac{3 3934}{7}

Alternative Form

a_{1} \approx - 26.880689, a_{2} \approx 26.880689

Show Solution