Solve -2(5x -1) 10x - 2 - Socratic AI (ScanMath)

Question

Simplify the expression

- 100 x^{2} + 20 x - 2

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- 2 (50 x^{2} - 10 x + 1)

Show Solution

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

Alternative Form

x_{1} = 0.1 - 0.1 i, x_{2} = 0.1 + 0.1 i

Evaluate

- 2 (5 x - 1) \times 10 x - 2

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

- 2 (5 x - 1) \times 10 x - 2 = 0

Multiply

More Steps

- 20 x (5 x - 1) - 2 = 0

Calculate

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- 100 x^{2} + 20 x - 2 = 0

Multiply both sides

100 x^{2} - 20 x + 2 = 0

Substitute a= 100,b= - 20 and c= 2 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{20 \pm ( - 20 ) ^{2} - 4 \times 100 \times 2}{2 \times 100}

Simplify the expression

x = \frac{20 \pm ( - 20 ) ^{2} - 4 \times 100 \times 2}{200}

Simplify the expression

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x = \frac{20 \pm - 400}{200}

Simplify the radical expression

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x = \frac{20 \pm 20 i}{200}

Separate the equation into 2 possible cases

x = \frac{20 + 20 i}{200} x = \frac{20 - 20 i}{200}

Simplify the expression

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x = \frac{1}{10} + \frac{1}{10} i x = \frac{20 - 20 i}{200}

Simplify the expression

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x = \frac{1}{10} + \frac{1}{10} i x = \frac{1}{10} - \frac{1}{10} i

Solution

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

Alternative Form

x_{1} = 0.1 - 0.1 i, x_{2} = 0.1 + 0.1 i

Show Solution