Solve 10x^2/54-152

Question

Simplify the expression

\frac{5 x ^{2} - 4104}{27}

Evaluate

(10 \times \frac{x ^{2}}{54}) - 152

Multiply the terms

More Steps

Multiply the terms

10 \times \frac{x ^{2}}{54}

Cancel out the common factor 2

5 \times \frac{x ^{2}}{27}

Multiply the terms

\frac{5 x ^{2}}{27}

\frac{5 x ^{2}}{27} - 152

Reduce fractions to a common denominator

\frac{5 x ^{2}}{27} - \frac{152 \times 27}{27}

Write all numerators above the common denominator

\frac{5 x ^{2} - 152 \times 27}{27}

Solution

\frac{5 x ^{2} - 4104}{27}

Show Solution

Find the roots

x_{1} = - \frac{6 570}{5}, x_{2} = \frac{6 570}{5}

Alternative Form

x_{1} \approx - 28.649607, x_{2} \approx 28.649607

Evaluate

(10 \times \frac{x ^{2}}{54}) - 152

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

(10 \times \frac{x ^{2}}{54}) - 152 = 0

Multiply the terms

More Steps

Multiply the terms

10 \times \frac{x ^{2}}{54}

Cancel out the common factor 2

5 \times \frac{x ^{2}}{27}

Multiply the terms

\frac{5 x ^{2}}{27}

\frac{5 x ^{2}}{27} - 152 = 0

Subtract the terms

More Steps

Simplify

\frac{5 x ^{2}}{27} - 152

Reduce fractions to a common denominator

\frac{5 x ^{2}}{27} - \frac{152 \times 27}{27}

Write all numerators above the common denominator

\frac{5 x ^{2} - 152 \times 27}{27}

Multiply the numbers

\frac{5 x ^{2} - 4104}{27}

\frac{5 x ^{2} - 4104}{27} = 0

Simplify

5 x^{2} - 4104 = 0

Move the constant to the right side

5 x^{2} = 4104

Divide both sides

\frac{5 x ^{2}}{5} = \frac{4104}{5}

Divide the numbers

x^{2} = \frac{4104}{5}

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

x = \pm \frac{4104}{5}

Simplify the expression

More Steps

Evaluate

\frac{4104}{5}

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

\frac{4104}{5}

Simplify the radical expression

More Steps

Evaluate

4104

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

36 \times 114

Write the number in exponential form with the base of 6

6^{2} \times 114

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

6^{2} \times 114

Reduce the index of the radical and exponent with 2

6114

\frac{6 114}{5}

Multiply by the Conjugate

\frac{6 114 \times 5}{5 \times 5}

Multiply the numbers

More Steps

Evaluate

114 \times 5

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

114 \times 5

Calculate the product

570

\frac{6 570}{5 \times 5}

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

\frac{6 570}{5}

x = \pm \frac{6 570}{5}

Separate the equation into 2 possible cases

x = \frac{6 570}{5} x = - \frac{6 570}{5}

Solution

x_{1} = - \frac{6 570}{5}, x_{2} = \frac{6 570}{5}

Alternative Form

x_{1} \approx - 28.649607, x_{2} \approx 28.649607

Show Solution