Solve 45/58x^2-9 - Socratic AI (ScanMath)

Question

Factor the expression

\frac{9}{58} (5 x^{2} - 58)

Evaluate

\frac{45}{58} x^{2} - 9

Solution

\frac{9}{58} (5 x^{2} - 58)

Show Solution

x_{1} = - \frac{290}{5}, x_{2} = \frac{290}{5}

Alternative Form

x_{1} \approx - 3.405877, x_{2} \approx 3.405877

Evaluate

\frac{45}{58} x^{2} - 9

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

\frac{45}{58} x^{2} - 9 = 0

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

\frac{45}{58} x^{2} = 0 + 9

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

\frac{45}{58} x^{2} = 9

Multiply by the reciprocal

\frac{45}{58} x^{2} \times \frac{58}{45} = 9 \times \frac{58}{45}

Multiply

x^{2} = 9 \times \frac{58}{45}

Multiply

More Steps

Evaluate

9 \times \frac{58}{45}

Reduce the numbers

1 \times \frac{58}{5}

Multiply the numbers

\frac{58}{5}

x^{2} = \frac{58}{5}

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

x = \pm \frac{58}{5}

Simplify the expression

More Steps

Evaluate

\frac{58}{5}

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

\frac{58}{5}

Multiply by the Conjugate

\frac{58 \times 5}{5 \times 5}

Multiply the numbers

More Steps

Evaluate

58 \times 5

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

58 \times 5

Calculate the product

290

\frac{290}{5 \times 5}

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

\frac{290}{5}

x = \pm \frac{290}{5}

Separate the equation into 2 possible cases

x = \frac{290}{5} x = - \frac{290}{5}

Solution

x_{1} = - \frac{290}{5}, x_{2} = \frac{290}{5}

Alternative Form

x_{1} \approx - 3.405877, x_{2} \approx 3.405877

Show Solution