Solve 2x^2-56/2x^2-18

Question

Simplify the expression

- 26 x^{2} - 18

Evaluate

2 x^{2} - \frac{56}{2} x^{2} - 18

Divide the terms

More Steps

Evaluate

\frac{56}{2}

Reduce the numbers

\frac{28}{1}

Calculate

28

2 x^{2} - 28 x^{2} - 18

Solution

More Steps

Evaluate

2 x^{2} - 28 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(2 - 28) x^{2}

Subtract the numbers

- 26 x^{2}

- 26 x^{2} - 18

Show Solution

Factor the expression

- 2 (13 x^{2} + 9)

Evaluate

2 x^{2} - \frac{56}{2} x^{2} - 18

Divide the terms

More Steps

Evaluate

\frac{56}{2}

Reduce the numbers

\frac{28}{1}

Calculate

28

2 x^{2} - 28 x^{2} - 18

Subtract the terms

More Steps

Simplify

2 x^{2} - 28 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(2 - 28) x^{2}

Subtract the numbers

- 26 x^{2}

- 26 x^{2} - 18

Solution

- 2 (13 x^{2} + 9)

Show Solution

Find the roots

x_{1} = - \frac{3 13}{13} i, x_{2} = \frac{3 13}{13} i

Alternative Form

x_{1} \approx - 0.83205 i, x_{2} \approx 0.83205 i

Evaluate

2 x^{2} - \frac{56}{2} x^{2} - 18

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

2 x^{2} - \frac{56}{2} x^{2} - 18 = 0

Divide the terms

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Evaluate

\frac{56}{2}

Reduce the numbers

\frac{28}{1}

Calculate

28

2 x^{2} - 28 x^{2} - 18 = 0

Subtract the terms

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Simplify

2 x^{2} - 28 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(2 - 28) x^{2}

Subtract the numbers

- 26 x^{2}

- 26 x^{2} - 18 = 0

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

- 26 x^{2} = 0 + 18

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

- 26 x^{2} = 18

Change the signs on both sides of the equation

26 x^{2} = - 18

Divide both sides

\frac{26 x ^{2}}{26} = \frac{- 18}{26}

Divide the numbers

x^{2} = \frac{- 18}{26}

Divide the numbers

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Evaluate

\frac{- 18}{26}

Cancel out the common factor 2

\frac{- 9}{13}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{9}{13}

x^{2} = - \frac{9}{13}

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

x = \pm - \frac{9}{13}

Simplify the expression

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Evaluate

- \frac{9}{13}

Evaluate the power

\frac{9}{13} \times - 1

Evaluate the power

\frac{9}{13} \times i

Evaluate the power

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Evaluate

\frac{9}{13}

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

\frac{9}{13}

Simplify the radical expression

\frac{3}{13}

Multiply by the Conjugate

\frac{3 13}{13 \times 13}

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

\frac{3 13}{13}

\frac{3 13}{13} i

x = \pm \frac{3 13}{13} i

Separate the equation into 2 possible cases

x = \frac{3 13}{13} i x = - \frac{3 13}{13} i

Solution

x_{1} = - \frac{3 13}{13} i, x_{2} = \frac{3 13}{13} i

Alternative Form

x_{1} \approx - 0.83205 i, x_{2} \approx 0.83205 i

Show Solution