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Simplifying t = -4.9t2 + 0t + 70 Anything times zero is zero. t = -4.9t2 + 0t + 70 Reorder the terms: t = 0 + 70 + -4.9t2 Combine like terms: 0 + 70 = 70 t = 70 + -4.9t2 Solving t = 70 + -4.9t2 Solving for variable 't'. Reorder the terms: -70 + t + 4.9t2 = 70 + -4.9t2 + -70 + 4.9t2 Reorder the terms: -70 + t + 4.9t2 = 70 + -70 + -4.9t2 + 4.9t2 Combine like terms: 70 + -70 = 0 -70 + t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -70 + t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -70 + t + 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'. -14.28571429 + 0.2040816327t + t2 = 0 Move the constant term to the right: Add '14.28571429' to each side of the equation. -14.28571429 + 0.2040816327t + 14.28571429 + t2 = 0 + 14.28571429 Reorder the terms: -14.28571429 + 14.28571429 + 0.2040816327t + t2 = 0 + 14.28571429 Combine like terms: -14.28571429 + 14.28571429 = 0.00000000 0.00000000 + 0.2040816327t + t2 = 0 + 14.28571429 0.2040816327t + t2 = 0 + 14.28571429 Combine like terms: 0 + 14.28571429 = 14.28571429 0.2040816327t + t2 = 14.28571429 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.2040816327t + 0.25 + t2 = 14.28571429 + 0.25 Reorder the terms: 0.25 + 0.2040816327t + t2 = 14.28571429 + 0.25 Combine like terms: 14.28571429 + 0.25 = 14.53571429 0.25 + 0.2040816327t + t2 = 14.53571429 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 14.53571429 Calculate the square root of the right side: 3.812573185 Break this problem into two subproblems by setting (t + 0.5) equal to 3.812573185 and -3.812573185.Subproblem 1
t + 0.5 = 3.812573185 Simplifying t + 0.5 = 3.812573185 Reorder the terms: 0.5 + t = 3.812573185 Solving 0.5 + t = 3.812573185 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 3.812573185 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 3.812573185 + -0.5 t = 3.812573185 + -0.5 Combine like terms: 3.812573185 + -0.5 = 3.312573185 t = 3.312573185 Simplifying t = 3.312573185Subproblem 2
t + 0.5 = -3.812573185 Simplifying t + 0.5 = -3.812573185 Reorder the terms: 0.5 + t = -3.812573185 Solving 0.5 + t = -3.812573185 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -3.812573185 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -3.812573185 + -0.5 t = -3.812573185 + -0.5 Combine like terms: -3.812573185 + -0.5 = -4.312573185 t = -4.312573185 Simplifying t = -4.312573185Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.312573185, -4.312573185}
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