Solve 4x^2-90126 - ScanMath

Question

Factor the expression

2 (2 x^{2} - 45063)

Evaluate

4 x^{2} - 90126

Solution

2 (2 x^{2} - 45063)

Show Solution

x_{1} = - \frac{3 10014}{2}, x_{2} = \frac{3 10014}{2}

Alternative Form

x_{1} \approx - 150.104963, x_{2} \approx 150.104963

Evaluate

4 x^{2} - 90126

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

4 x^{2} - 90126 = 0

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

4 x^{2} = 0 + 90126

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

4 x^{2} = 90126

Divide both sides

\frac{4 x ^{2}}{4} = \frac{90126}{4}

Divide the numbers

x^{2} = \frac{90126}{4}

Cancel out the common factor 2

x^{2} = \frac{45063}{2}

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

x = \pm \frac{45063}{2}

Simplify the expression

More Steps

Evaluate

\frac{45063}{2}

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

\frac{45063}{2}

Simplify the radical expression

More Steps

Evaluate

45063

Write the expression as a product where the root of one of the factors can be evaluated

9 \times 5007

Write the number in exponential form with the base of 3

3^{2} \times 5007

The root of a product is equal to the product of the roots of each factor

3^{2} \times 5007

Reduce the index of the radical and exponent with 2

35007

\frac{3 5007}{2}

Multiply by the Conjugate

\frac{3 5007 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

5007 \times 2

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

5007 \times 2

Calculate the product

10014

\frac{3 10014}{2 \times 2}

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

\frac{3 10014}{2}

x = \pm \frac{3 10014}{2}

Separate the equation into 2 possible cases

x = \frac{3 10014}{2} x = - \frac{3 10014}{2}

Solution

x_{1} = - \frac{3 10014}{2}, x_{2} = \frac{3 10014}{2}

Alternative Form

x_{1} \approx - 150.104963, x_{2} \approx 150.104963

Show Solution