Solve 3x^2-8 - ScanMath

Question

Find the roots

x_{1} = - \frac{2 6}{3}, x_{2} = \frac{2 6}{3}

Alternative Form

x_{1} \approx - 1.632993, x_{2} \approx 1.632993

Evaluate

3 x^{2} - 8

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

3 x^{2} - 8 = 0

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

3 x^{2} = 0 + 8

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

3 x^{2} = 8

Divide both sides

\frac{3 x ^{2}}{3} = \frac{8}{3}

Divide the numbers

x^{2} = \frac{8}{3}

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

x = \pm \frac{8}{3}

Simplify the expression

More Steps

Evaluate

\frac{8}{3}

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

\frac{8}{3}

Simplify the radical expression

More Steps

Evaluate

8

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

4 \times 2

Write the number in exponential form with the base of 2

2^{2} \times 2

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

2^{2} \times 2

Reduce the index of the radical and exponent with 2

22

\frac{2 2}{3}

Multiply by the Conjugate

\frac{2 2 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

2 \times 3

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

2 \times 3

Calculate the product

6

\frac{2 6}{3 \times 3}

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

\frac{2 6}{3}

x = \pm \frac{2 6}{3}

Separate the equation into 2 possible cases

x = \frac{2 6}{3} x = - \frac{2 6}{3}

Solution

x_{1} = - \frac{2 6}{3}, x_{2} = \frac{2 6}{3}

Alternative Form

x_{1} \approx - 1.632993, x_{2} \approx 1.632993

Show Solution