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Simplifying -1.86t2 + 15t + 25 = 0 Reorder the terms: 25 + 15t + -1.86t2 = 0 Solving 25 + 15t + -1.86t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1.86 the coefficient of the squared term: Divide each side by '-1.86'. -13.44086022 + -8.064516129t + t2 = 0 Move the constant term to the right: Add '13.44086022' to each side of the equation. -13.44086022 + -8.064516129t + 13.44086022 + t2 = 0 + 13.44086022 Reorder the terms: -13.44086022 + 13.44086022 + -8.064516129t + t2 = 0 + 13.44086022 Combine like terms: -13.44086022 + 13.44086022 = 0.00000000 0.00000000 + -8.064516129t + t2 = 0 + 13.44086022 -8.064516129t + t2 = 0 + 13.44086022 Combine like terms: 0 + 13.44086022 = 13.44086022 -8.064516129t + t2 = 13.44086022 The t term is -8.064516129t. Take half its coefficient (-4.032258065). Square it (16.25910510) and add it to both sides. Add '16.25910510' to each side of the equation. -8.064516129t + 16.25910510 + t2 = 13.44086022 + 16.25910510 Reorder the terms: 16.25910510 + -8.064516129t + t2 = 13.44086022 + 16.25910510 Combine like terms: 13.44086022 + 16.25910510 = 29.69996532 16.25910510 + -8.064516129t + t2 = 29.69996532 Factor a perfect square on the left side: (t + -4.032258065)(t + -4.032258065) = 29.69996532 Calculate the square root of the right side: 5.449767456 Break this problem into two subproblems by setting (t + -4.032258065) equal to 5.449767456 and -5.449767456.Subproblem 1
t + -4.032258065 = 5.449767456 Simplifying t + -4.032258065 = 5.449767456 Reorder the terms: -4.032258065 + t = 5.449767456 Solving -4.032258065 + t = 5.449767456 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.032258065' to each side of the equation. -4.032258065 + 4.032258065 + t = 5.449767456 + 4.032258065 Combine like terms: -4.032258065 + 4.032258065 = 0.000000000 0.000000000 + t = 5.449767456 + 4.032258065 t = 5.449767456 + 4.032258065 Combine like terms: 5.449767456 + 4.032258065 = 9.482025521 t = 9.482025521 Simplifying t = 9.482025521Subproblem 2
t + -4.032258065 = -5.449767456 Simplifying t + -4.032258065 = -5.449767456 Reorder the terms: -4.032258065 + t = -5.449767456 Solving -4.032258065 + t = -5.449767456 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.032258065' to each side of the equation. -4.032258065 + 4.032258065 + t = -5.449767456 + 4.032258065 Combine like terms: -4.032258065 + 4.032258065 = 0.000000000 0.000000000 + t = -5.449767456 + 4.032258065 t = -5.449767456 + 4.032258065 Combine like terms: -5.449767456 + 4.032258065 = -1.417509391 t = -1.417509391 Simplifying t = -1.417509391Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.482025521, -1.417509391}
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