Solve (a-2)2-2(a^2)

Question

Simplify the expression

2 a - 4 - 2 a^{2}

Show Solution

2 (a - 2 - a^{2})

Show Solution

a_{1} = \frac{1}{2} - \frac{7}{2} i, a_{2} = \frac{1}{2} + \frac{7}{2} i

Alternative Form

a_{1} \approx 0.5 - 1.322876 i, a_{2} \approx 0.5 + 1.322876 i

Evaluate

(a - 2) \times 2 - 2 (a^{2})

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

(a - 2) \times 2 - 2 (a^{2}) = 0

Calculate

(a - 2) \times 2 - 2 a^{2} = 0

Multiply the terms

2 (a - 2) - 2 a^{2} = 0

Calculate

More Steps

2 a - 4 - 2 a^{2} = 0

Rewrite in standard form

- 2 a^{2} + 2 a - 4 = 0

Multiply both sides

2 a^{2} - 2 a + 4 = 0

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

a = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 2 \times 4}{2 \times 2}

Simplify the expression

a = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 2 \times 4}{4}

Simplify the expression

More Steps

a = \frac{2 \pm - 28}{4}

Simplify the radical expression

More Steps

a = \frac{2 \pm 2 7 \times i}{4}

Separate the equation into 2 possible cases

a = \frac{2 + 2 7 \times i}{4} a = \frac{2 - 2 7 \times i}{4}

Simplify the expression

More Steps

a = \frac{1}{2} + \frac{7}{2} i a = \frac{2 - 2 7 \times i}{4}

Simplify the expression

More Steps

a = \frac{1}{2} + \frac{7}{2} i a = \frac{1}{2} - \frac{7}{2} i

Solution

a_{1} = \frac{1}{2} - \frac{7}{2} i, a_{2} = \frac{1}{2} + \frac{7}{2} i

Alternative Form

a_{1} \approx 0.5 - 1.322876 i, a_{2} \approx 0.5 + 1.322876 i

Show Solution