Solve (52)*x^2-10

Question

Factor the expression

2 (26 x^{2} - 5)

Evaluate

52 x^{2} - 10

Solution

2 (26 x^{2} - 5)

Show Solution

x_{1} = - \frac{130}{26}, x_{2} = \frac{130}{26}

Alternative Form

x_{1} \approx - 0.438529, x_{2} \approx 0.438529

Evaluate

52 x^{2} - 10

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

52 x^{2} - 10 = 0

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

52 x^{2} = 0 + 10

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

52 x^{2} = 10

Divide both sides

\frac{52 x ^{2}}{52} = \frac{10}{52}

Divide the numbers

x^{2} = \frac{10}{52}

Cancel out the common factor 2

x^{2} = \frac{5}{26}

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

x = \pm \frac{5}{26}

Simplify the expression

More Steps

Evaluate

\frac{5}{26}

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

\frac{5}{26}

Multiply by the Conjugate

\frac{5 \times 26}{26 \times 26}

Multiply the numbers

More Steps

Evaluate

5 \times 26

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

5 \times 26

Calculate the product

130

\frac{130}{26 \times 26}

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

\frac{130}{26}

x = \pm \frac{130}{26}

Separate the equation into 2 possible cases

x = \frac{130}{26} x = - \frac{130}{26}

Solution

x_{1} = - \frac{130}{26}, x_{2} = \frac{130}{26}

Alternative Form

x_{1} \approx - 0.438529, x_{2} \approx 0.438529

Show Solution