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Simplifying t2 + -1.5t + -10 = 0 Reorder the terms: -10 + -1.5t + t2 = 0 Solving -10 + -1.5t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -1.5t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -1.5t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1.5t + t2 = 0 + 10 -1.5t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -1.5t + t2 = 10 The t term is -1.5t. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5t + 0.5625 + t2 = 10 + 0.5625 Reorder the terms: 0.5625 + -1.5t + t2 = 10 + 0.5625 Combine like terms: 10 + 0.5625 = 10.5625 0.5625 + -1.5t + t2 = 10.5625 Factor a perfect square on the left side: (t + -0.75)(t + -0.75) = 10.5625 Calculate the square root of the right side: 3.25 Break this problem into two subproblems by setting (t + -0.75) equal to 3.25 and -3.25.Subproblem 1
t + -0.75 = 3.25 Simplifying t + -0.75 = 3.25 Reorder the terms: -0.75 + t = 3.25 Solving -0.75 + t = 3.25 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = 3.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = 3.25 + 0.75 t = 3.25 + 0.75 Combine like terms: 3.25 + 0.75 = 4 t = 4 Simplifying t = 4Subproblem 2
t + -0.75 = -3.25 Simplifying t + -0.75 = -3.25 Reorder the terms: -0.75 + t = -3.25 Solving -0.75 + t = -3.25 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = -3.25 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = -3.25 + 0.75 t = -3.25 + 0.75 Combine like terms: -3.25 + 0.75 = -2.5 t = -2.5 Simplifying t = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. t = {4, -2.5}
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