Solve 48x^2-6 - ScanMath

Question

Factor the expression

6 (8 x^{2} - 1)

Evaluate

48 x^{2} - 6

Solution

6 (8 x^{2} - 1)

Show Solution

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

Alternative Form

x_{1} \approx - 0.353553, x_{2} \approx 0.353553

Evaluate

48 x^{2} - 6

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

48 x^{2} - 6 = 0

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

48 x^{2} = 0 + 6

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

48 x^{2} = 6

Divide both sides

\frac{48 x ^{2}}{48} = \frac{6}{48}

Divide the numbers

x^{2} = \frac{6}{48}

Cancel out the common factor 6

x^{2} = \frac{1}{8}

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

x = \pm \frac{1}{8}

Simplify the expression

More Steps

Evaluate

\frac{1}{8}

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

\frac{1}{8}

Simplify the radical expression

\frac{1}{8}

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{1}{2 2}

Multiply by the Conjugate

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

Multiply the numbers

More Steps

Evaluate

22 \times 2

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

2 \times 2

Multiply the numbers

4

\frac{2}{4}

x = \pm \frac{2}{4}

Separate the equation into 2 possible cases

x = \frac{2}{4} x = - \frac{2}{4}

Solution

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

Alternative Form

x_{1} \approx - 0.353553, x_{2} \approx 0.353553

Show Solution