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Simplifying 100t2 + 100t + -2550 = 0 Reorder the terms: -2550 + 100t + 100t2 = 0 Solving -2550 + 100t + 100t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '50'. 50(-51 + 2t + 2t2) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(-51 + 2t + 2t2)' equal to zero and attempt to solve: Simplifying -51 + 2t + 2t2 = 0 Solving -51 + 2t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -25.5 + t + t2 = 0 Move the constant term to the right: Add '25.5' to each side of the equation. -25.5 + t + 25.5 + t2 = 0 + 25.5 Reorder the terms: -25.5 + 25.5 + t + t2 = 0 + 25.5 Combine like terms: -25.5 + 25.5 = 0.0 0.0 + t + t2 = 0 + 25.5 t + t2 = 0 + 25.5 Combine like terms: 0 + 25.5 = 25.5 t + t2 = 25.5 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 25.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 25.5 + 0.25 Combine like terms: 25.5 + 0.25 = 25.75 1.25 + t2 = 25.75 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 25.75 Calculate the square root of the right side: 5.074445783 Break this problem into two subproblems by setting (t + 0.5) equal to 5.074445783 and -5.074445783.Subproblem 1
t + 0.5 = 5.074445783 Simplifying t + 0.5 = 5.074445783 Reorder the terms: 0.5 + t = 5.074445783 Solving 0.5 + t = 5.074445783 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 5.074445783 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 5.074445783 + -0.5 t = 5.074445783 + -0.5 Combine like terms: 5.074445783 + -0.5 = 4.574445783 t = 4.574445783 Simplifying t = 4.574445783Subproblem 2
t + 0.5 = -5.074445783 Simplifying t + 0.5 = -5.074445783 Reorder the terms: 0.5 + t = -5.074445783 Solving 0.5 + t = -5.074445783 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -5.074445783 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -5.074445783 + -0.5 t = -5.074445783 + -0.5 Combine like terms: -5.074445783 + -0.5 = -5.574445783 t = -5.574445783 Simplifying t = -5.574445783Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.574445783, -5.574445783}Solution
t = {4.574445783, -5.574445783}
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