Solve (x-6)2 -x (x 8)=2

Question

Solve the equation(The real numbers system)

x \in / R

Alternative Form

No real solution

Show Solution

x_{1} = \frac{1}{8} - \frac{111}{8} i, x_{2} = \frac{1}{8} + \frac{111}{8} i

Alternative Form

x_{1} \approx 0.125 - 1.316957 i, x_{2} \approx 0.125 + 1.316957 i

Evaluate

(x - 6) \times 2 - x (x \times 8) = 2

Remove the parentheses

(x - 6) \times 2 - x \times x \times 8 = 2

Simplify

More Steps

2 (x - 6) - 8 x^{2} = 2

Expand the expression

More Steps

2 x - 12 - 8 x^{2} = 2

Move the expression to the left side

2 x - 14 - 8 x^{2} = 0

Rewrite in standard form

- 8 x^{2} + 2 x - 14 = 0

Multiply both sides

8 x^{2} - 2 x + 14 = 0

Substitute a= 8,b= - 2 and c= 14 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 8 \times 14}{2 \times 8}

Simplify the expression

x = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 8 \times 14}{16}

Simplify the expression

More Steps

x = \frac{2 \pm - 444}{16}

Simplify the radical expression

More Steps

x = \frac{2 \pm 2 111 \times i}{16}

Separate the equation into 2 possible cases

x = \frac{2 + 2 111 \times i}{16} x = \frac{2 - 2 111 \times i}{16}

Simplify the expression

More Steps

x = \frac{1}{8} + \frac{111}{8} i x = \frac{2 - 2 111 \times i}{16}

Simplify the expression

More Steps

x = \frac{1}{8} + \frac{111}{8} i x = \frac{1}{8} - \frac{111}{8} i

Solution

x_{1} = \frac{1}{8} - \frac{111}{8} i, x_{2} = \frac{1}{8} + \frac{111}{8} i

Alternative Form

x_{1} \approx 0.125 - 1.316957 i, x_{2} \approx 0.125 + 1.316957 i

Show Solution