Solve 17-3(x^2) - ScanMath

Question

Find the roots

x_{1} = - \frac{51}{3}, x_{2} = \frac{51}{3}

Alternative Form

x_{1} \approx - 2.380476, x_{2} \approx 2.380476

Evaluate

17 - 3 (x^{2})

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

17 - 3 (x^{2}) = 0

Calculate

17 - 3 x^{2} = 0

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

- 3 x^{2} = 0 - 17

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

- 3 x^{2} = - 17

Change the signs on both sides of the equation

3 x^{2} = 17

Divide both sides

\frac{3 x ^{2}}{3} = \frac{17}{3}

Divide the numbers

x^{2} = \frac{17}{3}

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

x = \pm \frac{17}{3}

Simplify the expression

More Steps

Evaluate

\frac{17}{3}

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

\frac{17}{3}

Multiply by the Conjugate

\frac{17 \times 3}{3 \times 3}

Multiply the numbers

More Steps

Evaluate

17 \times 3

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

17 \times 3

Calculate the product

51

\frac{51}{3 \times 3}

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

\frac{51}{3}

x = \pm \frac{51}{3}

Separate the equation into 2 possible cases

x = \frac{51}{3} x = - \frac{51}{3}

Solution

x_{1} = - \frac{51}{3}, x_{2} = \frac{51}{3}

Alternative Form

x_{1} \approx - 2.380476, x_{2} \approx 2.380476

Show Solution