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Simplifying 550 = (0.3t2) + 11.5t Reorder the terms: 550 = 11.5t + (0.3t2) Solving 550 = 11.5t + (0.3t2) Solving for variable 't'. Reorder the terms: 550 + -11.5t + (-0.3t2) = 11.5t + -11.5t + (0.3t2) + (-0.3t2) Combine like terms: 11.5t + -11.5t = 0.0 550 + -11.5t + (-0.3t2) = 0.0 + (0.3t2) + (-0.3t2) 550 + -11.5t + (-0.3t2) = (0.3t2) + (-0.3t2) Combine like terms: (0.3t2) + (-0.3t2) = 0.0 550 + -11.5t + (-0.3t2) = 0.0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. -1833.333333 + 38.33333333t + t2 = 0 Move the constant term to the right: Add '1833.333333' to each side of the equation. -1833.333333 + 38.33333333t + 1833.333333 + t2 = 0 + 1833.333333 Reorder the terms: -1833.333333 + 1833.333333 + 38.33333333t + t2 = 0 + 1833.333333 Combine like terms: -1833.333333 + 1833.333333 = 0.000000 0.000000 + 38.33333333t + t2 = 0 + 1833.333333 38.33333333t + t2 = 0 + 1833.333333 Combine like terms: 0 + 1833.333333 = 1833.333333 38.33333333t + t2 = 1833.333333 The t term is 38.33333333t. Take half its coefficient (19.16666667). Square it (367.3611112) and add it to both sides. Add '367.3611112' to each side of the equation. 38.33333333t + 367.3611112 + t2 = 1833.333333 + 367.3611112 Reorder the terms: 367.3611112 + 38.33333333t + t2 = 1833.333333 + 367.3611112 Combine like terms: 1833.333333 + 367.3611112 = 2200.6944442 367.3611112 + 38.33333333t + t2 = 2200.6944442 Factor a perfect square on the left side: ((t) + 19.16666667)((t) + 19.16666667) = 2200.6944442 Calculate the square root of the right side: 46.911559814 Break this problem into two subproblems by setting ((t) + 19.16666667) equal to 46.911559814 and -46.911559814.Subproblem 1
(t) + 19.16666667 = 46.911559814 Simplifying (t) + 19.16666667 = 46.911559814 t + 19.16666667 = 46.911559814 Reorder the terms: 19.16666667 + t = 46.911559814 Solving 19.16666667 + t = 46.911559814 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-19.16666667' to each side of the equation. 19.16666667 + -19.16666667 + t = 46.911559814 + -19.16666667 Combine like terms: 19.16666667 + -19.16666667 = 0.00000000 0.00000000 + t = 46.911559814 + -19.16666667 t = 46.911559814 + -19.16666667 Combine like terms: 46.911559814 + -19.16666667 = 27.744893144 t = 27.744893144 Simplifying t = 27.744893144Subproblem 2
(t) + 19.16666667 = -46.911559814 Simplifying (t) + 19.16666667 = -46.911559814 t + 19.16666667 = -46.911559814 Reorder the terms: 19.16666667 + t = -46.911559814 Solving 19.16666667 + t = -46.911559814 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-19.16666667' to each side of the equation. 19.16666667 + -19.16666667 + t = -46.911559814 + -19.16666667 Combine like terms: 19.16666667 + -19.16666667 = 0.00000000 0.00000000 + t = -46.911559814 + -19.16666667 t = -46.911559814 + -19.16666667 Combine like terms: -46.911559814 + -19.16666667 = -66.078226484 t = -66.078226484 Simplifying t = -66.078226484Solution
The solution to the problem is based on the solutions from the subproblems. t = {27.744893144, -66.078226484}
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