Solve (13x^2-48) - ScanMath

Question

Find the roots

x_{1} = - \frac{4 39}{13}, x_{2} = \frac{4 39}{13}

Alternative Form

x_{1} \approx - 1.921538, x_{2} \approx 1.921538

Evaluate

(13 x^{2} - 48)

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

13 x^{2} - 48 = 0

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

13 x^{2} = 0 + 48

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

13 x^{2} = 48

Divide both sides

\frac{13 x ^{2}}{13} = \frac{48}{13}

Divide the numbers

x^{2} = \frac{48}{13}

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

x = \pm \frac{48}{13}

Simplify the expression

More Steps

Evaluate

\frac{48}{13}

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

\frac{48}{13}

Simplify the radical expression

More Steps

Evaluate

48

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

16 \times 3

Write the number in exponential form with the base of 4

4^{2} \times 3

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

4^{2} \times 3

Reduce the index of the radical and exponent with 2

43

\frac{4 3}{13}

Multiply by the Conjugate

\frac{4 3 \times 13}{13 \times 13}

Multiply the numbers

More Steps

Evaluate

3 \times 13

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

3 \times 13

Calculate the product

39

\frac{4 39}{13 \times 13}

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

\frac{4 39}{13}

x = \pm \frac{4 39}{13}

Separate the equation into 2 possible cases

x = \frac{4 39}{13} x = - \frac{4 39}{13}

Solution

x_{1} = - \frac{4 39}{13}, x_{2} = \frac{4 39}{13}

Alternative Form

x_{1} \approx - 1.921538, x_{2} \approx 1.921538

Show Solution