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Simplifying -5t2 + 7t = 0.6 Reorder the terms: 7t + -5t2 = 0.6 Solving 7t + -5t2 = 0.6 Solving for variable 't'. Reorder the terms: -0.6 + 7t + -5t2 = 0.6 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 -0.6 + 7t + -5t2 = 0.0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 0.12 + -1.4t + t2 = 0.0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -1.4t + -0.12 + t2 = 0.0 + -0.12 Reorder the terms: 0.12 + -0.12 + -1.4t + t2 = 0.0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -1.4t + t2 = 0.0 + -0.12 -1.4t + t2 = 0.0 + -0.12 Combine like terms: 0.0 + -0.12 = -0.12 -1.4t + t2 = -0.12 The t term is -1.4t. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4t + 0.49 + t2 = -0.12 + 0.49 Reorder the terms: 0.49 + -1.4t + t2 = -0.12 + 0.49 Combine like terms: -0.12 + 0.49 = 0.37 0.49 + -1.4t + t2 = 0.37 Factor a perfect square on the left side: (t + -0.7)(t + -0.7) = 0.37 Calculate the square root of the right side: 0.608276253 Break this problem into two subproblems by setting (t + -0.7) equal to 0.608276253 and -0.608276253.Subproblem 1
t + -0.7 = 0.608276253 Simplifying t + -0.7 = 0.608276253 Reorder the terms: -0.7 + t = 0.608276253 Solving -0.7 + t = 0.608276253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + t = 0.608276253 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = 0.608276253 + 0.7 t = 0.608276253 + 0.7 Combine like terms: 0.608276253 + 0.7 = 1.308276253 t = 1.308276253 Simplifying t = 1.308276253Subproblem 2
t + -0.7 = -0.608276253 Simplifying t + -0.7 = -0.608276253 Reorder the terms: -0.7 + t = -0.608276253 Solving -0.7 + t = -0.608276253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + t = -0.608276253 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = -0.608276253 + 0.7 t = -0.608276253 + 0.7 Combine like terms: -0.608276253 + 0.7 = 0.091723747 t = 0.091723747 Simplifying t = 0.091723747Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.308276253, 0.091723747}
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