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Simplifying -4t2 + 13t + 7 = 0 Reorder the terms: 7 + 13t + -4t2 = 0 Solving 7 + 13t + -4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.75 + -3.25t + t2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -3.25t + 1.75 + t2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -3.25t + t2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -3.25t + t2 = 0 + 1.75 -3.25t + t2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -3.25t + t2 = 1.75 The t term is -3.25t. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25t + 2.640625 + t2 = 1.75 + 2.640625 Reorder the terms: 2.640625 + -3.25t + t2 = 1.75 + 2.640625 Combine like terms: 1.75 + 2.640625 = 4.390625 2.640625 + -3.25t + t2 = 4.390625 Factor a perfect square on the left side: (t + -1.625)(t + -1.625) = 4.390625 Calculate the square root of the right side: 2.095381827 Break this problem into two subproblems by setting (t + -1.625) equal to 2.095381827 and -2.095381827.Subproblem 1
t + -1.625 = 2.095381827 Simplifying t + -1.625 = 2.095381827 Reorder the terms: -1.625 + t = 2.095381827 Solving -1.625 + t = 2.095381827 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + t = 2.095381827 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + t = 2.095381827 + 1.625 t = 2.095381827 + 1.625 Combine like terms: 2.095381827 + 1.625 = 3.720381827 t = 3.720381827 Simplifying t = 3.720381827Subproblem 2
t + -1.625 = -2.095381827 Simplifying t + -1.625 = -2.095381827 Reorder the terms: -1.625 + t = -2.095381827 Solving -1.625 + t = -2.095381827 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + t = -2.095381827 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + t = -2.095381827 + 1.625 t = -2.095381827 + 1.625 Combine like terms: -2.095381827 + 1.625 = -0.470381827 t = -0.470381827 Simplifying t = -0.470381827Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.720381827, -0.470381827}
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