Solve -7x-1 -7x-1 3 2x 1 x-4 -1/2 4 -1/2 5/2

Question

Simplify the expression

- 14 x - \frac{33}{4} - 132 x^{2}

Show Solution

- \frac{1}{4} (56 x + 33 + 528 x^{2})

Show Solution

x_{1} = - \frac{7}{132} - \frac{65}{33} i, x_{2} = - \frac{7}{132} + \frac{65}{33} i

Alternative Form

x_{1} \approx - 0.05 \dot{3} \dot{0} - 0.244311 i, x_{2} \approx - 0.05 \dot{3} \dot{0} + 0.244311 i

Evaluate

- 7 x - 1 - 7 x - 132 x \times 1 \times x - 4 - \frac{1}{2} \times 4 - \frac{1}{2} \times \frac{5}{2}

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

- 7 x - 1 - 7 x - 132 x \times 1 \times x - 4 - \frac{1}{2} \times 4 - \frac{1}{2} \times \frac{5}{2} = 0

Multiply the terms

More Steps

- 7 x - 1 - 7 x - 132 x^{2} - 4 - \frac{1}{2} \times 4 - \frac{1}{2} \times \frac{5}{2} = 0

Subtract the terms

More Steps

- 14 x - 1 - 132 x^{2} - 4 - \frac{1}{2} \times 4 - \frac{1}{2} \times \frac{5}{2} = 0

Multiply the numbers

More Steps

- 14 x - 1 - 132 x^{2} - 4 - 2 - \frac{1}{2} \times \frac{5}{2} = 0

Subtract the numbers

- 14 x - 5 - 132 x^{2} - 2 - \frac{1}{2} \times \frac{5}{2} = 0

Multiply the numbers

More Steps

- 14 x - 5 - 132 x^{2} - 2 - \frac{5}{4} = 0

Subtract the numbers

- 14 x - 7 - 132 x^{2} - \frac{5}{4} = 0

Subtract the numbers

More Steps

- 14 x - \frac{33}{4} - 132 x^{2} = 0

Rewrite in standard form

- 132 x^{2} - 14 x - \frac{33}{4} = 0

Multiply both sides

132 x^{2} + 14 x + \frac{33}{4} = 0

Multiply both sides

4 (132 x^{2} + 14 x + \frac{33}{4}) = 4 \times 0

Calculate

528 x^{2} + 56 x + 33 = 0

Substitute a= 528,b= 56 and c= 33 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 56 \pm 5 6 ^{2} - 4 \times 528 \times 33}{2 \times 528}

Simplify the expression

x = \frac{- 56 \pm 5 6 ^{2} - 4 \times 528 \times 33}{1056}

Simplify the expression

More Steps

x = \frac{- 56 \pm - 66560}{1056}

Simplify the radical expression

More Steps

x = \frac{- 56 \pm 32 65 \times i}{1056}

Separate the equation into 2 possible cases

x = \frac{- 56 + 32 65 \times i}{1056} x = \frac{- 56 - 32 65 \times i}{1056}

Simplify the expression

More Steps

x = - \frac{7}{132} + \frac{65}{33} i x = \frac{- 56 - 32 65 \times i}{1056}

Simplify the expression

More Steps

x = - \frac{7}{132} + \frac{65}{33} i x = - \frac{7}{132} - \frac{65}{33} i

Solution

x_{1} = - \frac{7}{132} - \frac{65}{33} i, x_{2} = - \frac{7}{132} + \frac{65}{33} i

Alternative Form

x_{1} \approx - 0.05 \dot{3} \dot{0} - 0.244311 i, x_{2} \approx - 0.05 \dot{3} \dot{0} + 0.244311 i

Show Solution