Solve 4x 12x-7 - ScanMath

Question

Simplify the expression

48 x^{2} - 7

Evaluate

4 x \times 12 x - 7

Solution

More Steps

Evaluate

4 x \times 12 x

Multiply the terms

48 x \times x

Multiply the terms

48 x^{2}

48 x^{2} - 7

Show Solution

x_{1} = - \frac{21}{12}, x_{2} = \frac{21}{12}

Alternative Form

x_{1} \approx - 0.381881, x_{2} \approx 0.381881

Evaluate

4 x \times 12 x - 7

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

4 x \times 12 x - 7 = 0

Multiply

More Steps

Multiply the terms

4 x \times 12 x

Multiply the terms

48 x \times x

Multiply the terms

48 x^{2}

48 x^{2} - 7 = 0

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

48 x^{2} = 0 + 7

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

48 x^{2} = 7

Divide both sides

\frac{48 x ^{2}}{48} = \frac{7}{48}

Divide the numbers

x^{2} = \frac{7}{48}

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

x = \pm \frac{7}{48}

Simplify the expression

More Steps

Evaluate

\frac{7}{48}

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

\frac{7}{48}

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{7}{4 3}

Multiply by the Conjugate

\frac{7 \times 3}{4 3 \times 3}

Multiply the numbers

More Steps

Evaluate

7 \times 3

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

7 \times 3

Calculate the product

21

\frac{21}{4 3 \times 3}

Multiply the numbers

More Steps

Evaluate

43 \times 3

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

4 \times 3

Multiply the terms

12

\frac{21}{12}

x = \pm \frac{21}{12}

Separate the equation into 2 possible cases

x = \frac{21}{12} x = - \frac{21}{12}

Solution

x_{1} = - \frac{21}{12}, x_{2} = \frac{21}{12}

Alternative Form

x_{1} \approx - 0.381881, x_{2} \approx 0.381881

Show Solution