Solve 24/63x^2-5 - ScanMath

Question

Simplify the expression

\frac{8}{21} x^{2} - 5

Evaluate

\frac{24}{63} x^{2} - 5

Solution

\frac{8}{21} x^{2} - 5

Show Solution

\frac{1}{21} (8 x^{2} - 105)

Evaluate

\frac{24}{63} x^{2} - 5

Cancel out the common factor 3

\frac{8}{21} x^{2} - 5

Solution

\frac{1}{21} (8 x^{2} - 105)

Show Solution

x_{1} = - \frac{210}{4}, x_{2} = \frac{210}{4}

Alternative Form

x_{1} \approx - 3.622844, x_{2} \approx 3.622844

Evaluate

\frac{24}{63} x^{2} - 5

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

\frac{24}{63} x^{2} - 5 = 0

Cancel out the common factor 3

\frac{8}{21} x^{2} - 5 = 0

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

\frac{8}{21} x^{2} = 0 + 5

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

\frac{8}{21} x^{2} = 5

Multiply by the reciprocal

\frac{8}{21} x^{2} \times \frac{21}{8} = 5 \times \frac{21}{8}

Multiply

x^{2} = 5 \times \frac{21}{8}

Multiply

More Steps

Evaluate

5 \times \frac{21}{8}

Multiply the numbers

\frac{5 \times 21}{8}

Multiply the numbers

\frac{105}{8}

x^{2} = \frac{105}{8}

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

x = \pm \frac{105}{8}

Simplify the expression

More Steps

Evaluate

\frac{105}{8}

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

\frac{105}{8}

Simplify the radical expression

More Steps

Evaluate

8

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

4 \times 2

Write the number in exponential form with the base of 2

2^{2} \times 2

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

2^{2} \times 2

Reduce the index of the radical and exponent with 2

22

\frac{105}{2 2}

Multiply by the Conjugate

\frac{105 \times 2}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

105 \times 2

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

105 \times 2

Calculate the product

210

\frac{210}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

22 \times 2

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

2 \times 2

Multiply the numbers

4

\frac{210}{4}

x = \pm \frac{210}{4}

Separate the equation into 2 possible cases

x = \frac{210}{4} x = - \frac{210}{4}

Solution

x_{1} = - \frac{210}{4}, x_{2} = \frac{210}{4}

Alternative Form

x_{1} \approx - 3.622844, x_{2} \approx 3.622844

Show Solution