Solve t^2-30t-225/2

Question

Factor the expression

\frac{1}{2} (2 t^{2} - 60 t - 225)

Show Solution

t_{1} = \frac{30 - 15 6}{2}, t_{2} = \frac{30 + 15 6}{2}

Alternative Form

t_{1} \approx - 3.371173, t_{2} \approx 33.371173

Evaluate

t^{2} - 30 t - \frac{225}{2}

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

t^{2} - 30 t - \frac{225}{2} = 0

Multiply both sides

2 (t^{2} - 30 t - \frac{225}{2}) = 2 \times 0

Calculate

2 t^{2} - 60 t - 225 = 0

Substitute a= 2,b= - 60 and c= - 225 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{60 \pm ( - 60 ) ^{2} - 4 \times 2 ( - 225 )}{2 \times 2}

Simplify the expression

t = \frac{60 \pm ( - 60 ) ^{2} - 4 \times 2 ( - 225 )}{4}

Simplify the expression

More Steps

t = \frac{60 \pm 5400}{4}

Simplify the radical expression

More Steps

t = \frac{60 \pm 30 6}{4}

Separate the equation into 2 possible cases

t = \frac{60 + 30 6}{4} t = \frac{60 - 30 6}{4}

Simplify the expression

More Steps

t = \frac{30 + 15 6}{2} t = \frac{60 - 30 6}{4}

Simplify the expression

More Steps

t = \frac{30 + 15 6}{2} t = \frac{30 - 15 6}{2}

Solution

t_{1} = \frac{30 - 15 6}{2}, t_{2} = \frac{30 + 15 6}{2}

Alternative Form

t_{1} \approx - 3.371173, t_{2} \approx 33.371173

Show Solution