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Simplifying -5t2 + 10t + 50 = 0 Reorder the terms: 50 + 10t + -5t2 = 0 Solving 50 + 10t + -5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(10 + 2t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(10 + 2t + -1t2)' equal to zero and attempt to solve: Simplifying 10 + 2t + -1t2 = 0 Solving 10 + 2t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -2t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -2t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -2t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -2t + t2 = 0 + 10 -2t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -2t + t2 = 10 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 10 + 1 Reorder the terms: 1 + -2t + t2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + -2t + t2 = 11 Factor a perfect square on the left side: (t + -1)(t + -1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (t + -1) equal to 3.31662479 and -3.31662479.Subproblem 1
t + -1 = 3.31662479 Simplifying t + -1 = 3.31662479 Reorder the terms: -1 + t = 3.31662479 Solving -1 + t = 3.31662479 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + t = 3.31662479 + 1 t = 3.31662479 + 1 Combine like terms: 3.31662479 + 1 = 4.31662479 t = 4.31662479 Simplifying t = 4.31662479Subproblem 2
t + -1 = -3.31662479 Simplifying t + -1 = -3.31662479 Reorder the terms: -1 + t = -3.31662479 Solving -1 + t = -3.31662479 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + t = -3.31662479 + 1 t = -3.31662479 + 1 Combine like terms: -3.31662479 + 1 = -2.31662479 t = -2.31662479 Simplifying t = -2.31662479Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.31662479, -2.31662479}Solution
t = {4.31662479, -2.31662479}
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