Solve 6/x^2-19=1 - ScanMath

Question

Solve the equation

x_{1} = - \frac{30}{10}, x_{2} = \frac{30}{10}

Alternative Form

x_{1} \approx - 0.547723, x_{2} \approx 0.547723

Evaluate

\frac{6}{x ^{2}} - 19 = 1

Find the domain

More Steps

Evaluate

x^{2} \neq = 0

The only way a power can not be 0 is when the base not equals 0

x \neq = 0

\frac{6}{x ^{2}} - 19 = 1, x \neq = 0

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

\frac{6}{x ^{2}} = 1 + 19

Add the numbers

\frac{6}{x ^{2}} = 20

Cross multiply

6 = x^{2} \times 20

Simplify the equation

6 = 20 x^{2}

Rewrite the expression

2 \times 3 = 2 \times 10 x^{2}

Evaluate

3 = 10 x^{2}

Swap the sides of the equation

10 x^{2} = 3

Divide both sides

\frac{10 x ^{2}}{10} = \frac{3}{10}

Divide the numbers

x^{2} = \frac{3}{10}

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

x = \pm \frac{3}{10}

Simplify the expression

More Steps

Evaluate

\frac{3}{10}

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

\frac{3}{10}

Multiply by the Conjugate

\frac{3 \times 10}{10 \times 10}

Multiply the numbers

More Steps

Evaluate

3 \times 10

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

3 \times 10

Calculate the product

30

\frac{30}{10 \times 10}

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

\frac{30}{10}

x = \pm \frac{30}{10}

Separate the equation into 2 possible cases

x = \frac{30}{10} x = - \frac{30}{10}

Check if the solution is in the defined range

x = \frac{30}{10} x = - \frac{30}{10}, x \neq = 0

Find the intersection of the solution and the defined range

x = \frac{30}{10} x = - \frac{30}{10}

Solution

x_{1} = - \frac{30}{10}, x_{2} = \frac{30}{10}

Alternative Form

x_{1} \approx - 0.547723, x_{2} \approx 0.547723

Show Solution