Solve (2x^25)2 - (2x^2 - 5)2

Question

Simplify the expression

16 x^{2} + 10

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2 (8 x^{2} + 5)

Show Solution

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

Alternative Form

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

Evaluate

(2 x^{2} \times 5) \times 2 - (2 x^{2} - 5) \times 2

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

(2 x^{2} \times 5) \times 2 - (2 x^{2} - 5) \times 2 = 0

Multiply the terms

10 x^{2} \times 2 - (2 x^{2} - 5) \times 2 = 0

Multiply the numbers

20 x^{2} - (2 x^{2} - 5) \times 2 = 0

Multiply the terms

20 x^{2} - 2 (2 x^{2} - 5) = 0

Calculate

More Steps

16 x^{2} + 10 = 0

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

16 x^{2} = 0 - 10

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

16 x^{2} = - 10

Divide both sides

\frac{16 x ^{2}}{16} = \frac{- 10}{16}

Divide the numbers

x^{2} = \frac{- 10}{16}

Divide the numbers

More Steps

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

More Steps

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

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

Show Solution