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Simplifying 56 = 15t + 3t2 Solving 56 = 15t + 3t2 Solving for variable 't'. Reorder the terms: 56 + -15t + -3t2 = 15t + -15t + 3t2 + -3t2 Combine like terms: 15t + -15t = 0 56 + -15t + -3t2 = 0 + 3t2 + -3t2 56 + -15t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 56 + -15t + -3t2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -18.66666667 + 5t + t2 = 0 Move the constant term to the right: Add '18.66666667' to each side of the equation. -18.66666667 + 5t + 18.66666667 + t2 = 0 + 18.66666667 Reorder the terms: -18.66666667 + 18.66666667 + 5t + t2 = 0 + 18.66666667 Combine like terms: -18.66666667 + 18.66666667 = 0.00000000 0.00000000 + 5t + t2 = 0 + 18.66666667 5t + t2 = 0 + 18.66666667 Combine like terms: 0 + 18.66666667 = 18.66666667 5t + t2 = 18.66666667 The t term is 5t. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5t + 6.25 + t2 = 18.66666667 + 6.25 Reorder the terms: 6.25 + 5t + t2 = 18.66666667 + 6.25 Combine like terms: 18.66666667 + 6.25 = 24.91666667 6.25 + 5t + t2 = 24.91666667 Factor a perfect square on the left side: (t + 2.5)(t + 2.5) = 24.91666667 Calculate the square root of the right side: 4.991659711 Break this problem into two subproblems by setting (t + 2.5) equal to 4.991659711 and -4.991659711.Subproblem 1
t + 2.5 = 4.991659711 Simplifying t + 2.5 = 4.991659711 Reorder the terms: 2.5 + t = 4.991659711 Solving 2.5 + t = 4.991659711 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = 4.991659711 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = 4.991659711 + -2.5 t = 4.991659711 + -2.5 Combine like terms: 4.991659711 + -2.5 = 2.491659711 t = 2.491659711 Simplifying t = 2.491659711Subproblem 2
t + 2.5 = -4.991659711 Simplifying t + 2.5 = -4.991659711 Reorder the terms: 2.5 + t = -4.991659711 Solving 2.5 + t = -4.991659711 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + t = -4.991659711 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + t = -4.991659711 + -2.5 t = -4.991659711 + -2.5 Combine like terms: -4.991659711 + -2.5 = -7.491659711 t = -7.491659711 Simplifying t = -7.491659711Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.491659711, -7.491659711}
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