Solve (4x^2) (6/3) - 5

Question

Simplify the expression

8 x^{2} - 5

Evaluate

4 x^{2} (\frac{6}{3}) - 5

Divide the terms

More Steps

Evaluate

\frac{6}{3}

Reduce the numbers

\frac{2}{1}

Calculate

2

4 x^{2} \times 2 - 5

Solution

8 x^{2} - 5

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Find the roots

x_{1} = - \frac{10}{4}, x_{2} = \frac{10}{4}

Alternative Form

x_{1} \approx - 0.790569, x_{2} \approx 0.790569

Evaluate

(4 x^{2}) (\frac{6}{3}) - 5

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

(4 x^{2}) (\frac{6}{3}) - 5 = 0

Multiply the terms

4 x^{2} (\frac{6}{3}) - 5 = 0

Divide the terms

More Steps

Evaluate

\frac{6}{3}

Reduce the numbers

\frac{2}{1}

Calculate

2

4 x^{2} \times 2 - 5 = 0

Multiply the numbers

8 x^{2} - 5 = 0

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

8 x^{2} = 0 + 5

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

8 x^{2} = 5

Divide both sides

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

Divide the numbers

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

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

x = \pm \frac{5}{8}

Simplify the expression

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Evaluate

\frac{5}{8}

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

\frac{5}{8}

Simplify the radical expression

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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{5}{2 2}

Multiply by the Conjugate

\frac{5 \times 2}{2 2 \times 2}

Multiply the numbers

More Steps

Evaluate

5 \times 2

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

5 \times 2

Calculate the product

10

\frac{10}{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{10}{4}

x = \pm \frac{10}{4}

Separate the equation into 2 possible cases

x = \frac{10}{4} x = - \frac{10}{4}

Solution

x_{1} = - \frac{10}{4}, x_{2} = \frac{10}{4}

Alternative Form

x_{1} \approx - 0.790569, x_{2} \approx 0.790569

Show Solution