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Simplifying 0 = -7t2 + 12t + 25 Reorder the terms: 0 = 25 + 12t + -7t2 Solving 0 = 25 + 12t + -7t2 Solving for variable 't'. Combine like terms: 0 + -25 = -25 -25 + -12t + 7t2 = 25 + 12t + -7t2 + -25 + -12t + 7t2 Reorder the terms: -25 + -12t + 7t2 = 25 + -25 + 12t + -12t + -7t2 + 7t2 Combine like terms: 25 + -25 = 0 -25 + -12t + 7t2 = 0 + 12t + -12t + -7t2 + 7t2 -25 + -12t + 7t2 = 12t + -12t + -7t2 + 7t2 Combine like terms: 12t + -12t = 0 -25 + -12t + 7t2 = 0 + -7t2 + 7t2 -25 + -12t + 7t2 = -7t2 + 7t2 Combine like terms: -7t2 + 7t2 = 0 -25 + -12t + 7t2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.571428571 + -1.714285714t + t2 = 0 Move the constant term to the right: Add '3.571428571' to each side of the equation. -3.571428571 + -1.714285714t + 3.571428571 + t2 = 0 + 3.571428571 Reorder the terms: -3.571428571 + 3.571428571 + -1.714285714t + t2 = 0 + 3.571428571 Combine like terms: -3.571428571 + 3.571428571 = 0.000000000 0.000000000 + -1.714285714t + t2 = 0 + 3.571428571 -1.714285714t + t2 = 0 + 3.571428571 Combine like terms: 0 + 3.571428571 = 3.571428571 -1.714285714t + t2 = 3.571428571 The t term is -1.714285714t. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714t + 0.7346938773 + t2 = 3.571428571 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714t + t2 = 3.571428571 + 0.7346938773 Combine like terms: 3.571428571 + 0.7346938773 = 4.3061224483 0.7346938773 + -1.714285714t + t2 = 4.3061224483 Factor a perfect square on the left side: (t + -0.857142857)(t + -0.857142857) = 4.3061224483 Calculate the square root of the right side: 2.075119864 Break this problem into two subproblems by setting (t + -0.857142857) equal to 2.075119864 and -2.075119864.Subproblem 1
t + -0.857142857 = 2.075119864 Simplifying t + -0.857142857 = 2.075119864 Reorder the terms: -0.857142857 + t = 2.075119864 Solving -0.857142857 + t = 2.075119864 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + t = 2.075119864 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + t = 2.075119864 + 0.857142857 t = 2.075119864 + 0.857142857 Combine like terms: 2.075119864 + 0.857142857 = 2.932262721 t = 2.932262721 Simplifying t = 2.932262721Subproblem 2
t + -0.857142857 = -2.075119864 Simplifying t + -0.857142857 = -2.075119864 Reorder the terms: -0.857142857 + t = -2.075119864 Solving -0.857142857 + t = -2.075119864 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.857142857' to each side of the equation. -0.857142857 + 0.857142857 + t = -2.075119864 + 0.857142857 Combine like terms: -0.857142857 + 0.857142857 = 0.000000000 0.000000000 + t = -2.075119864 + 0.857142857 t = -2.075119864 + 0.857142857 Combine like terms: -2.075119864 + 0.857142857 = -1.217977007 t = -1.217977007 Simplifying t = -1.217977007Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.932262721, -1.217977007}
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