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Simplifying t = -4.9t2 + 24.5t + 9.7 Reorder the terms: t = 9.7 + 24.5t + -4.9t2 Solving t = 9.7 + 24.5t + -4.9t2 Solving for variable 't'. Reorder the terms: -9.7 + t + -24.5t + 4.9t2 = 9.7 + 24.5t + -4.9t2 + -9.7 + -24.5t + 4.9t2 Combine like terms: t + -24.5t = -23.5t -9.7 + -23.5t + 4.9t2 = 9.7 + 24.5t + -4.9t2 + -9.7 + -24.5t + 4.9t2 Reorder the terms: -9.7 + -23.5t + 4.9t2 = 9.7 + -9.7 + 24.5t + -24.5t + -4.9t2 + 4.9t2 Combine like terms: 9.7 + -9.7 = 0.0 -9.7 + -23.5t + 4.9t2 = 0.0 + 24.5t + -24.5t + -4.9t2 + 4.9t2 -9.7 + -23.5t + 4.9t2 = 24.5t + -24.5t + -4.9t2 + 4.9t2 Combine like terms: 24.5t + -24.5t = 0.0 -9.7 + -23.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -9.7 + -23.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -9.7 + -23.5t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -1.979591837 + -4.795918367t + t2 = 0 Move the constant term to the right: Add '1.979591837' to each side of the equation. -1.979591837 + -4.795918367t + 1.979591837 + t2 = 0 + 1.979591837 Reorder the terms: -1.979591837 + 1.979591837 + -4.795918367t + t2 = 0 + 1.979591837 Combine like terms: -1.979591837 + 1.979591837 = 0.000000000 0.000000000 + -4.795918367t + t2 = 0 + 1.979591837 -4.795918367t + t2 = 0 + 1.979591837 Combine like terms: 0 + 1.979591837 = 1.979591837 -4.795918367t + t2 = 1.979591837 The t term is -4.795918367t. Take half its coefficient (-2.397959184). Square it (5.750208248) and add it to both sides. Add '5.750208248' to each side of the equation. -4.795918367t + 5.750208248 + t2 = 1.979591837 + 5.750208248 Reorder the terms: 5.750208248 + -4.795918367t + t2 = 1.979591837 + 5.750208248 Combine like terms: 1.979591837 + 5.750208248 = 7.729800085 5.750208248 + -4.795918367t + t2 = 7.729800085 Factor a perfect square on the left side: (t + -2.397959184)(t + -2.397959184) = 7.729800085 Calculate the square root of the right side: 2.780251802 Break this problem into two subproblems by setting (t + -2.397959184) equal to 2.780251802 and -2.780251802.Subproblem 1
t + -2.397959184 = 2.780251802 Simplifying t + -2.397959184 = 2.780251802 Reorder the terms: -2.397959184 + t = 2.780251802 Solving -2.397959184 + t = 2.780251802 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.397959184' to each side of the equation. -2.397959184 + 2.397959184 + t = 2.780251802 + 2.397959184 Combine like terms: -2.397959184 + 2.397959184 = 0.000000000 0.000000000 + t = 2.780251802 + 2.397959184 t = 2.780251802 + 2.397959184 Combine like terms: 2.780251802 + 2.397959184 = 5.178210986 t = 5.178210986 Simplifying t = 5.178210986Subproblem 2
t + -2.397959184 = -2.780251802 Simplifying t + -2.397959184 = -2.780251802 Reorder the terms: -2.397959184 + t = -2.780251802 Solving -2.397959184 + t = -2.780251802 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.397959184' to each side of the equation. -2.397959184 + 2.397959184 + t = -2.780251802 + 2.397959184 Combine like terms: -2.397959184 + 2.397959184 = 0.000000000 0.000000000 + t = -2.780251802 + 2.397959184 t = -2.780251802 + 2.397959184 Combine like terms: -2.780251802 + 2.397959184 = -0.382292618 t = -0.382292618 Simplifying t = -0.382292618Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.178210986, -0.382292618}
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