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Simplifying t = -2t2 + 87t + 90 Reorder the terms: t = 90 + 87t + -2t2 Solving t = 90 + 87t + -2t2 Solving for variable 't'. Reorder the terms: -90 + t + -87t + 2t2 = 90 + 87t + -2t2 + -90 + -87t + 2t2 Combine like terms: t + -87t = -86t -90 + -86t + 2t2 = 90 + 87t + -2t2 + -90 + -87t + 2t2 Reorder the terms: -90 + -86t + 2t2 = 90 + -90 + 87t + -87t + -2t2 + 2t2 Combine like terms: 90 + -90 = 0 -90 + -86t + 2t2 = 0 + 87t + -87t + -2t2 + 2t2 -90 + -86t + 2t2 = 87t + -87t + -2t2 + 2t2 Combine like terms: 87t + -87t = 0 -90 + -86t + 2t2 = 0 + -2t2 + 2t2 -90 + -86t + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 -90 + -86t + 2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -43t + t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -43t + t2)' equal to zero and attempt to solve: Simplifying -45 + -43t + t2 = 0 Solving -45 + -43t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + -43t + 45 + t2 = 0 + 45 Reorder the terms: -45 + 45 + -43t + t2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -43t + t2 = 0 + 45 -43t + t2 = 0 + 45 Combine like terms: 0 + 45 = 45 -43t + t2 = 45 The t term is -43t. Take half its coefficient (-21.5). Square it (462.25) and add it to both sides. Add '462.25' to each side of the equation. -43t + 462.25 + t2 = 45 + 462.25 Reorder the terms: 462.25 + -43t + t2 = 45 + 462.25 Combine like terms: 45 + 462.25 = 507.25 462.25 + -43t + t2 = 507.25 Factor a perfect square on the left side: (t + -21.5)(t + -21.5) = 507.25 Calculate the square root of the right side: 22.522211259 Break this problem into two subproblems by setting (t + -21.5) equal to 22.522211259 and -22.522211259.Subproblem 1
t + -21.5 = 22.522211259 Simplifying t + -21.5 = 22.522211259 Reorder the terms: -21.5 + t = 22.522211259 Solving -21.5 + t = 22.522211259 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '21.5' to each side of the equation. -21.5 + 21.5 + t = 22.522211259 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + t = 22.522211259 + 21.5 t = 22.522211259 + 21.5 Combine like terms: 22.522211259 + 21.5 = 44.022211259 t = 44.022211259 Simplifying t = 44.022211259Subproblem 2
t + -21.5 = -22.522211259 Simplifying t + -21.5 = -22.522211259 Reorder the terms: -21.5 + t = -22.522211259 Solving -21.5 + t = -22.522211259 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '21.5' to each side of the equation. -21.5 + 21.5 + t = -22.522211259 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + t = -22.522211259 + 21.5 t = -22.522211259 + 21.5 Combine like terms: -22.522211259 + 21.5 = -1.022211259 t = -1.022211259 Simplifying t = -1.022211259Solution
The solution to the problem is based on the solutions from the subproblems. t = {44.022211259, -1.022211259}Solution
t = {44.022211259, -1.022211259}
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