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Simplifying -20t2 + 450t + -300 = 0 Reorder the terms: -300 + 450t + -20t2 = 0 Solving -300 + 450t + -20t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '10'. 10(-30 + 45t + -2t2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-30 + 45t + -2t2)' equal to zero and attempt to solve: Simplifying -30 + 45t + -2t2 = 0 Solving -30 + 45t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 15 + -22.5t + t2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -22.5t + -15 + t2 = 0 + -15 Reorder the terms: 15 + -15 + -22.5t + t2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -22.5t + t2 = 0 + -15 -22.5t + t2 = 0 + -15 Combine like terms: 0 + -15 = -15 -22.5t + t2 = -15 The t term is -22.5t. Take half its coefficient (-11.25). Square it (126.5625) and add it to both sides. Add '126.5625' to each side of the equation. -22.5t + 126.5625 + t2 = -15 + 126.5625 Reorder the terms: 126.5625 + -22.5t + t2 = -15 + 126.5625 Combine like terms: -15 + 126.5625 = 111.5625 126.5625 + -22.5t + t2 = 111.5625 Factor a perfect square on the left side: (t + -11.25)(t + -11.25) = 111.5625 Calculate the square root of the right side: 10.562315087 Break this problem into two subproblems by setting (t + -11.25) equal to 10.562315087 and -10.562315087.Subproblem 1
t + -11.25 = 10.562315087 Simplifying t + -11.25 = 10.562315087 Reorder the terms: -11.25 + t = 10.562315087 Solving -11.25 + t = 10.562315087 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + t = 10.562315087 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + t = 10.562315087 + 11.25 t = 10.562315087 + 11.25 Combine like terms: 10.562315087 + 11.25 = 21.812315087 t = 21.812315087 Simplifying t = 21.812315087Subproblem 2
t + -11.25 = -10.562315087 Simplifying t + -11.25 = -10.562315087 Reorder the terms: -11.25 + t = -10.562315087 Solving -11.25 + t = -10.562315087 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.25' to each side of the equation. -11.25 + 11.25 + t = -10.562315087 + 11.25 Combine like terms: -11.25 + 11.25 = 0.00 0.00 + t = -10.562315087 + 11.25 t = -10.562315087 + 11.25 Combine like terms: -10.562315087 + 11.25 = 0.687684913 t = 0.687684913 Simplifying t = 0.687684913Solution
The solution to the problem is based on the solutions from the subproblems. t = {21.812315087, 0.687684913}Solution
t = {21.812315087, 0.687684913}
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