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Simplifying t2 + 15t + -8 = 0 Reorder the terms: -8 + 15t + t2 = 0 Solving -8 + 15t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 15t + 8 + t2 = 0 + 8 Reorder the terms: -8 + 8 + 15t + t2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 15t + t2 = 0 + 8 15t + t2 = 0 + 8 Combine like terms: 0 + 8 = 8 15t + t2 = 8 The t term is 15t. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15t + 56.25 + t2 = 8 + 56.25 Reorder the terms: 56.25 + 15t + t2 = 8 + 56.25 Combine like terms: 8 + 56.25 = 64.25 56.25 + 15t + t2 = 64.25 Factor a perfect square on the left side: (t + 7.5)(t + 7.5) = 64.25 Calculate the square root of the right side: 8.015609771 Break this problem into two subproblems by setting (t + 7.5) equal to 8.015609771 and -8.015609771.Subproblem 1
t + 7.5 = 8.015609771 Simplifying t + 7.5 = 8.015609771 Reorder the terms: 7.5 + t = 8.015609771 Solving 7.5 + t = 8.015609771 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = 8.015609771 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = 8.015609771 + -7.5 t = 8.015609771 + -7.5 Combine like terms: 8.015609771 + -7.5 = 0.515609771 t = 0.515609771 Simplifying t = 0.515609771Subproblem 2
t + 7.5 = -8.015609771 Simplifying t + 7.5 = -8.015609771 Reorder the terms: 7.5 + t = -8.015609771 Solving 7.5 + t = -8.015609771 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = -8.015609771 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = -8.015609771 + -7.5 t = -8.015609771 + -7.5 Combine like terms: -8.015609771 + -7.5 = -15.515609771 t = -15.515609771 Simplifying t = -15.515609771Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.515609771, -15.515609771}
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