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Simplifying 0 = 59 + 12.5t + -4.9t2 Solving 0 = 59 + 12.5t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -59 = -59 -59 + -12.5t + 4.9t2 = 59 + 12.5t + -4.9t2 + -59 + -12.5t + 4.9t2 Reorder the terms: -59 + -12.5t + 4.9t2 = 59 + -59 + 12.5t + -12.5t + -4.9t2 + 4.9t2 Combine like terms: 59 + -59 = 0 -59 + -12.5t + 4.9t2 = 0 + 12.5t + -12.5t + -4.9t2 + 4.9t2 -59 + -12.5t + 4.9t2 = 12.5t + -12.5t + -4.9t2 + 4.9t2 Combine like terms: 12.5t + -12.5t = 0.0 -59 + -12.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -59 + -12.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -59 + -12.5t + 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'. -12.04081633 + -2.551020408t + t2 = 0 Move the constant term to the right: Add '12.04081633' to each side of the equation. -12.04081633 + -2.551020408t + 12.04081633 + t2 = 0 + 12.04081633 Reorder the terms: -12.04081633 + 12.04081633 + -2.551020408t + t2 = 0 + 12.04081633 Combine like terms: -12.04081633 + 12.04081633 = 0.00000000 0.00000000 + -2.551020408t + t2 = 0 + 12.04081633 -2.551020408t + t2 = 0 + 12.04081633 Combine like terms: 0 + 12.04081633 = 12.04081633 -2.551020408t + t2 = 12.04081633 The t term is -2.551020408t. Take half its coefficient (-1.275510204). Square it (1.626926281) and add it to both sides. Add '1.626926281' to each side of the equation. -2.551020408t + 1.626926281 + t2 = 12.04081633 + 1.626926281 Reorder the terms: 1.626926281 + -2.551020408t + t2 = 12.04081633 + 1.626926281 Combine like terms: 12.04081633 + 1.626926281 = 13.667742611 1.626926281 + -2.551020408t + t2 = 13.667742611 Factor a perfect square on the left side: (t + -1.275510204)(t + -1.275510204) = 13.667742611 Calculate the square root of the right side: 3.696991021 Break this problem into two subproblems by setting (t + -1.275510204) equal to 3.696991021 and -3.696991021.Subproblem 1
t + -1.275510204 = 3.696991021 Simplifying t + -1.275510204 = 3.696991021 Reorder the terms: -1.275510204 + t = 3.696991021 Solving -1.275510204 + t = 3.696991021 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.275510204' to each side of the equation. -1.275510204 + 1.275510204 + t = 3.696991021 + 1.275510204 Combine like terms: -1.275510204 + 1.275510204 = 0.000000000 0.000000000 + t = 3.696991021 + 1.275510204 t = 3.696991021 + 1.275510204 Combine like terms: 3.696991021 + 1.275510204 = 4.972501225 t = 4.972501225 Simplifying t = 4.972501225Subproblem 2
t + -1.275510204 = -3.696991021 Simplifying t + -1.275510204 = -3.696991021 Reorder the terms: -1.275510204 + t = -3.696991021 Solving -1.275510204 + t = -3.696991021 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.275510204' to each side of the equation. -1.275510204 + 1.275510204 + t = -3.696991021 + 1.275510204 Combine like terms: -1.275510204 + 1.275510204 = 0.000000000 0.000000000 + t = -3.696991021 + 1.275510204 t = -3.696991021 + 1.275510204 Combine like terms: -3.696991021 + 1.275510204 = -2.421480817 t = -2.421480817 Simplifying t = -2.421480817Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.972501225, -2.421480817}
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