Solve 1/2*25*20=1/2(t-25)*4(t-25)

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

t_{1} = 25 - 55, t_{2} = 25 + 55

Alternative Form

t_{1} \approx 13.81966, t_{2} \approx 36.18034

Evaluate

\frac{1}{2} \times 25 \times 20 = \frac{1}{2} (t - 25) \times 4 (t - 25)

Multiply the terms

More Steps

250 = \frac{1}{2} (t - 25) \times 4 (t - 25)

Multiply the terms

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250 = 2 (t - 25)^{2}

Swap the sides

2 (t - 25)^{2} = 250

Expand the expression

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2 t^{2} - 100 t + 1250 = 250

Move the expression to the left side

2 t^{2} - 100 t + 1000 = 0

Substitute a= 2,b= - 100 and c= 1000 into the quadratic formula t = \frac{- b \pm b ^{2} - 4 a c}{2 a}

t = \frac{100 \pm ( - 100 ) ^{2} - 4 \times 2 \times 1000}{2 \times 2}

Simplify the expression

t = \frac{100 \pm ( - 100 ) ^{2} - 4 \times 2 \times 1000}{4}

Simplify the expression

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t = \frac{100 \pm 2000}{4}

Simplify the radical expression

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t = \frac{100 \pm 20 5}{4}

Separate the equation into 2 possible cases

t = \frac{100 + 20 5}{4} t = \frac{100 - 20 5}{4}

Simplify the expression

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t = 25 + 55 t = \frac{100 - 20 5}{4}

Simplify the expression

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t = 25 + 55 t = 25 - 55

Solution

t_{1} = 25 - 55, t_{2} = 25 + 55

Alternative Form

t_{1} \approx 13.81966, t_{2} \approx 36.18034

Show Solution