Solve 5x ^ 2 - 48 - 4

Question

Simplify the expression

Solution

5 x^{2} - 52

Evaluate

5 x^{2} - 48 - 4

Solution

5 x^{2} - 52

Show Solution

Find the roots of the algebra expression

x_{1} = - \frac{2 65}{5}, x_{2} = \frac{2 65}{5}

Alternative Form

x_{1} \approx - 3.224903, x_{2} \approx 3.224903

Evaluate

5 x^{2} - 48 - 4

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

5 x^{2} - 48 - 4 = 0

Subtract the numbers

5 x^{2} - 52 = 0

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

5 x^{2} = 0 + 52

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

5 x^{2} = 52

Divide both sides

\frac{5 x ^{2}}{5} = \frac{52}{5}

Divide the numbers

x^{2} = \frac{52}{5}

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

x = \pm \frac{52}{5}

Simplify the expression

More Steps

Evaluate

\frac{52}{5}

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

\frac{52}{5}

Simplify the radical expression

More Steps

Evaluate

52

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

4 \times 13

Write the number in exponential form with the base of 2

2^{2} \times 13

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

2^{2} \times 13

Reduce the index of the radical and exponent with 2

213

\frac{2 13}{5}

Multiply by the Conjugate

\frac{2 13 \times 5}{5 \times 5}

Multiply the numbers

More Steps

Evaluate

13 \times 5

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

13 \times 5

Calculate the product

65

\frac{2 65}{5 \times 5}

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

\frac{2 65}{5}

x = \pm \frac{2 65}{5}

Separate the equation into 2 possible cases

x = \frac{2 65}{5} x = - \frac{2 65}{5}

Solution

x_{1} = - \frac{2 65}{5}, x_{2} = \frac{2 65}{5}

Alternative Form

x_{1} \approx - 3.224903, x_{2} \approx 3.224903

Show Solution