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Simplifying -4t2 + 7t + 10 = 0 Reorder the terms: 10 + 7t + -4t2 = 0 Solving 10 + 7t + -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'. -2.5 + -1.75t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -1.75t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -1.75t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -1.75t + t2 = 0 + 2.5 -1.75t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -1.75t + t2 = 2.5 The t term is -1.75t. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75t + 0.765625 + t2 = 2.5 + 0.765625 Reorder the terms: 0.765625 + -1.75t + t2 = 2.5 + 0.765625 Combine like terms: 2.5 + 0.765625 = 3.265625 0.765625 + -1.75t + t2 = 3.265625 Factor a perfect square on the left side: (t + -0.875)(t + -0.875) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (t + -0.875) equal to 1.807104037 and -1.807104037.Subproblem 1
t + -0.875 = 1.807104037 Simplifying t + -0.875 = 1.807104037 Reorder the terms: -0.875 + t = 1.807104037 Solving -0.875 + t = 1.807104037 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + t = 1.807104037 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = 1.807104037 + 0.875 t = 1.807104037 + 0.875 Combine like terms: 1.807104037 + 0.875 = 2.682104037 t = 2.682104037 Simplifying t = 2.682104037Subproblem 2
t + -0.875 = -1.807104037 Simplifying t + -0.875 = -1.807104037 Reorder the terms: -0.875 + t = -1.807104037 Solving -0.875 + t = -1.807104037 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + t = -1.807104037 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + t = -1.807104037 + 0.875 t = -1.807104037 + 0.875 Combine like terms: -1.807104037 + 0.875 = -0.932104037 t = -0.932104037 Simplifying t = -0.932104037Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.682104037, -0.932104037}
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