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Simplifying 15t2 + 15t + 700 = 11000 Reorder the terms: 700 + 15t + 15t2 = 11000 Solving 700 + 15t + 15t2 = 11000 Solving for variable 't'. Reorder the terms: 700 + -11000 + 15t + 15t2 = 11000 + -11000 Combine like terms: 700 + -11000 = -10300 -10300 + 15t + 15t2 = 11000 + -11000 Combine like terms: 11000 + -11000 = 0 -10300 + 15t + 15t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-2060 + 3t + 3t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2060 + 3t + 3t2)' equal to zero and attempt to solve: Simplifying -2060 + 3t + 3t2 = 0 Solving -2060 + 3t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -686.6666667 + t + t2 = 0 Move the constant term to the right: Add '686.6666667' to each side of the equation. -686.6666667 + t + 686.6666667 + t2 = 0 + 686.6666667 Reorder the terms: -686.6666667 + 686.6666667 + t + t2 = 0 + 686.6666667 Combine like terms: -686.6666667 + 686.6666667 = 0.0000000 0.0000000 + t + t2 = 0 + 686.6666667 t + t2 = 0 + 686.6666667 Combine like terms: 0 + 686.6666667 = 686.6666667 t + t2 = 686.6666667 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 = 686.6666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 686.6666667 + 0.25 Combine like terms: 686.6666667 + 0.25 = 686.9166667 1.25 + t2 = 686.9166667 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 686.9166667 Calculate the square root of the right side: 26.209095114 Break this problem into two subproblems by setting (t + 0.5) equal to 26.209095114 and -26.209095114.Subproblem 1
t + 0.5 = 26.209095114 Simplifying t + 0.5 = 26.209095114 Reorder the terms: 0.5 + t = 26.209095114 Solving 0.5 + t = 26.209095114 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 = 26.209095114 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 26.209095114 + -0.5 t = 26.209095114 + -0.5 Combine like terms: 26.209095114 + -0.5 = 25.709095114 t = 25.709095114 Simplifying t = 25.709095114Subproblem 2
t + 0.5 = -26.209095114 Simplifying t + 0.5 = -26.209095114 Reorder the terms: 0.5 + t = -26.209095114 Solving 0.5 + t = -26.209095114 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 = -26.209095114 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -26.209095114 + -0.5 t = -26.209095114 + -0.5 Combine like terms: -26.209095114 + -0.5 = -26.709095114 t = -26.709095114 Simplifying t = -26.709095114Solution
The solution to the problem is based on the solutions from the subproblems. t = {25.709095114, -26.709095114}Solution
t = {25.709095114, -26.709095114}
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