Solve (1015)*x^2 - 23

Question

Find the roots

x_{1} = - \frac{23345}{1015}, x_{2} = \frac{23345}{1015}

Alternative Form

x_{1} \approx - 0.150533, x_{2} \approx 0.150533

Evaluate

1015 x^{2} - 23

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

1015 x^{2} - 23 = 0

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

1015 x^{2} = 0 + 23

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

1015 x^{2} = 23

Divide both sides

\frac{1015 x ^{2}}{1015} = \frac{23}{1015}

Divide the numbers

x^{2} = \frac{23}{1015}

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

x = \pm \frac{23}{1015}

Simplify the expression

More Steps

Evaluate

\frac{23}{1015}

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

\frac{23}{1015}

Multiply by the Conjugate

\frac{23 \times 1015}{1015 \times 1015}

Multiply the numbers

More Steps

Evaluate

23 \times 1015

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

23 \times 1015

Calculate the product

23345

\frac{23345}{1015 \times 1015}

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

\frac{23345}{1015}

x = \pm \frac{23345}{1015}

Separate the equation into 2 possible cases

x = \frac{23345}{1015} x = - \frac{23345}{1015}

Solution

x_{1} = - \frac{23345}{1015}, x_{2} = \frac{23345}{1015}

Alternative Form

x_{1} \approx - 0.150533, x_{2} \approx 0.150533

Show Solution