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Simplifying 26.39t + t2 = 90 Solving 26.39t + t2 = 90 Solving for variable 't'. Reorder the terms: -90 + 26.39t + t2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + 26.39t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 26.39t + 90 + t2 = 0 + 90 Reorder the terms: -90 + 90 + 26.39t + t2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 26.39t + t2 = 0 + 90 26.39t + t2 = 0 + 90 Combine like terms: 0 + 90 = 90 26.39t + t2 = 90 The t term is 26.39t. Take half its coefficient (13.195). Square it (174.108025) and add it to both sides. Add '174.108025' to each side of the equation. 26.39t + 174.108025 + t2 = 90 + 174.108025 Reorder the terms: 174.108025 + 26.39t + t2 = 90 + 174.108025 Combine like terms: 90 + 174.108025 = 264.108025 174.108025 + 26.39t + t2 = 264.108025 Factor a perfect square on the left side: (t + 13.195)(t + 13.195) = 264.108025 Calculate the square root of the right side: 16.251400709 Break this problem into two subproblems by setting (t + 13.195) equal to 16.251400709 and -16.251400709.Subproblem 1
t + 13.195 = 16.251400709 Simplifying t + 13.195 = 16.251400709 Reorder the terms: 13.195 + t = 16.251400709 Solving 13.195 + t = 16.251400709 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-13.195' to each side of the equation. 13.195 + -13.195 + t = 16.251400709 + -13.195 Combine like terms: 13.195 + -13.195 = 0.000 0.000 + t = 16.251400709 + -13.195 t = 16.251400709 + -13.195 Combine like terms: 16.251400709 + -13.195 = 3.056400709 t = 3.056400709 Simplifying t = 3.056400709Subproblem 2
t + 13.195 = -16.251400709 Simplifying t + 13.195 = -16.251400709 Reorder the terms: 13.195 + t = -16.251400709 Solving 13.195 + t = -16.251400709 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-13.195' to each side of the equation. 13.195 + -13.195 + t = -16.251400709 + -13.195 Combine like terms: 13.195 + -13.195 = 0.000 0.000 + t = -16.251400709 + -13.195 t = -16.251400709 + -13.195 Combine like terms: -16.251400709 + -13.195 = -29.446400709 t = -29.446400709 Simplifying t = -29.446400709Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.056400709, -29.446400709}
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