Solve 10t - 2t t = 45

Question

Solve the equation(The real numbers system)

t \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

t_{1} = \frac{5}{2} - \frac{65}{2} i, t_{2} = \frac{5}{2} + \frac{65}{2} i

Alternative Form

t_{1} \approx 2.5 - 4.031129 i, t_{2} \approx 2.5 + 4.031129 i

Evaluate

10 t - 2 t \times t = 45

Multiply the terms

10 t - 2 t^{2} = 45

Move the expression to the left side

10 t - 2 t^{2} - 45 = 0

Rewrite in standard form

- 2 t^{2} + 10 t - 45 = 0

Multiply both sides

2 t^{2} - 10 t + 45 = 0

Substitute a= 2,b= - 10 and c= 45 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{10 \pm ( - 10 ) ^{2} - 4 \times 2 \times 45}{2 \times 2}

Simplify the expression

t = \frac{10 \pm ( - 10 ) ^{2} - 4 \times 2 \times 45}{4}

Simplify the expression

More Steps

t = \frac{10 \pm - 260}{4}

Simplify the radical expression

More Steps

t = \frac{10 \pm 2 65 \times i}{4}

Separate the equation into 2 possible cases

t = \frac{10 + 2 65 \times i}{4} t = \frac{10 - 2 65 \times i}{4}

Simplify the expression

More Steps

t = \frac{5}{2} + \frac{65}{2} i t = \frac{10 - 2 65 \times i}{4}

Simplify the expression

More Steps

t = \frac{5}{2} + \frac{65}{2} i t = \frac{5}{2} - \frac{65}{2} i

Solution

t_{1} = \frac{5}{2} - \frac{65}{2} i, t_{2} = \frac{5}{2} + \frac{65}{2} i

Alternative Form

t_{1} \approx 2.5 - 4.031129 i, t_{2} \approx 2.5 + 4.031129 i

Show Solution