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Simplifying -0.2t2 + 12t + -90 = 0 Reorder the terms: -90 + 12t + -0.2t2 = 0 Solving -90 + 12t + -0.2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 450 + -60t + t2 = 0 Move the constant term to the right: Add '-450' to each side of the equation. 450 + -60t + -450 + t2 = 0 + -450 Reorder the terms: 450 + -450 + -60t + t2 = 0 + -450 Combine like terms: 450 + -450 = 0 0 + -60t + t2 = 0 + -450 -60t + t2 = 0 + -450 Combine like terms: 0 + -450 = -450 -60t + t2 = -450 The t term is -60t. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60t + 900 + t2 = -450 + 900 Reorder the terms: 900 + -60t + t2 = -450 + 900 Combine like terms: -450 + 900 = 450 900 + -60t + t2 = 450 Factor a perfect square on the left side: (t + -30)(t + -30) = 450 Calculate the square root of the right side: 21.213203436 Break this problem into two subproblems by setting (t + -30) equal to 21.213203436 and -21.213203436.Subproblem 1
t + -30 = 21.213203436 Simplifying t + -30 = 21.213203436 Reorder the terms: -30 + t = 21.213203436 Solving -30 + t = 21.213203436 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + t = 21.213203436 + 30 Combine like terms: -30 + 30 = 0 0 + t = 21.213203436 + 30 t = 21.213203436 + 30 Combine like terms: 21.213203436 + 30 = 51.213203436 t = 51.213203436 Simplifying t = 51.213203436Subproblem 2
t + -30 = -21.213203436 Simplifying t + -30 = -21.213203436 Reorder the terms: -30 + t = -21.213203436 Solving -30 + t = -21.213203436 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + t = -21.213203436 + 30 Combine like terms: -30 + 30 = 0 0 + t = -21.213203436 + 30 t = -21.213203436 + 30 Combine like terms: -21.213203436 + 30 = 8.786796564 t = 8.786796564 Simplifying t = 8.786796564Solution
The solution to the problem is based on the solutions from the subproblems. t = {51.213203436, 8.786796564}
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