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Simplifying -0.01t2 + 0.7t + -10 = 0 Reorder the terms: -10 + 0.7t + -0.01t2 = 0 Solving -10 + 0.7t + -0.01t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. 1000 + -70t + t2 = 0 Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + -70t + -1000 + t2 = 0 + -1000 Reorder the terms: 1000 + -1000 + -70t + t2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -70t + t2 = 0 + -1000 -70t + t2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -70t + t2 = -1000 The t term is -70t. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70t + 1225 + t2 = -1000 + 1225 Reorder the terms: 1225 + -70t + t2 = -1000 + 1225 Combine like terms: -1000 + 1225 = 225 1225 + -70t + t2 = 225 Factor a perfect square on the left side: (t + -35)(t + -35) = 225 Calculate the square root of the right side: 15 Break this problem into two subproblems by setting (t + -35) equal to 15 and -15.Subproblem 1
t + -35 = 15 Simplifying t + -35 = 15 Reorder the terms: -35 + t = 15 Solving -35 + t = 15 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + t = 15 + 35 Combine like terms: -35 + 35 = 0 0 + t = 15 + 35 t = 15 + 35 Combine like terms: 15 + 35 = 50 t = 50 Simplifying t = 50Subproblem 2
t + -35 = -15 Simplifying t + -35 = -15 Reorder the terms: -35 + t = -15 Solving -35 + t = -15 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + t = -15 + 35 Combine like terms: -35 + 35 = 0 0 + t = -15 + 35 t = -15 + 35 Combine like terms: -15 + 35 = 20 t = 20 Simplifying t = 20Solution
The solution to the problem is based on the solutions from the subproblems. t = {50, 20}
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