Solve (5/2)x-3=-(x-2)^2 4

Question

Solve the equation(The real numbers system)

x \in / R

Alternative Form

No real solution

Show Solution

Solve using the quadratic formula in the complex numbers system

Solve by completing the square in the complex numbers system

Solve using the PQ formula in the complex numbers system

x_{1} = \frac{27}{16} - \frac{103}{16} i, x_{2} = \frac{27}{16} + \frac{103}{16} i

Alternative Form

x_{1} \approx 1.6875 - 0.634306 i, x_{2} \approx 1.6875 + 0.634306 i

Evaluate

\frac{5}{2} x - 3 = - (x - 2)^{2} \times 4

Use the commutative property to reorder the terms

\frac{5}{2} x - 3 = - 4 (x - 2)^{2}

Swap the sides

- 4 (x - 2)^{2} = \frac{5}{2} x - 3

Expand the expression

More Steps

- 4 x^{2} + 16 x - 16 = \frac{5}{2} x - 3

Move the expression to the left side

- 4 x^{2} + \frac{27}{2} x - 13 = 0

Multiply both sides

4 x^{2} - \frac{27}{2} x + 13 = 0

Multiply both sides

2 (4 x^{2} - \frac{27}{2} x + 13) = 2 \times 0

Calculate

8 x^{2} - 27 x + 26 = 0

Substitute a= 8,b= - 27 and c= 26 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{27 \pm ( - 27 ) ^{2} - 4 \times 8 \times 26}{2 \times 8}

Simplify the expression

x = \frac{27 \pm ( - 27 ) ^{2} - 4 \times 8 \times 26}{16}

Simplify the expression

More Steps

x = \frac{27 \pm - 103}{16}

Simplify the radical expression

More Steps

x = \frac{27 \pm 103 \times i}{16}

Separate the equation into 2 possible cases

x = \frac{27 + 103 \times i}{16} x = \frac{27 - 103 \times i}{16}

Simplify the expression

x = \frac{27}{16} + \frac{103}{16} i x = \frac{27 - 103 \times i}{16}

Simplify the expression

x = \frac{27}{16} + \frac{103}{16} i x = \frac{27}{16} - \frac{103}{16} i

Solution

x_{1} = \frac{27}{16} - \frac{103}{16} i, x_{2} = \frac{27}{16} + \frac{103}{16} i

Alternative Form

x_{1} \approx 1.6875 - 0.634306 i, x_{2} \approx 1.6875 + 0.634306 i

Show Solution