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Simplifying -2.7t2 + 23t + 9 = 0 Reorder the terms: 9 + 23t + -2.7t2 = 0 Solving 9 + 23t + -2.7t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -2.7 the coefficient of the squared term: Divide each side by '-2.7'. -3.333333333 + -8.518518519t + t2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -8.518518519t + 3.333333333 + t2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -8.518518519t + t2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -8.518518519t + t2 = 0 + 3.333333333 -8.518518519t + t2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -8.518518519t + t2 = 3.333333333 The t term is -8.518518519t. Take half its coefficient (-4.25925926). Square it (18.14128944) and add it to both sides. Add '18.14128944' to each side of the equation. -8.518518519t + 18.14128944 + t2 = 3.333333333 + 18.14128944 Reorder the terms: 18.14128944 + -8.518518519t + t2 = 3.333333333 + 18.14128944 Combine like terms: 3.333333333 + 18.14128944 = 21.474622773 18.14128944 + -8.518518519t + t2 = 21.474622773 Factor a perfect square on the left side: (t + -4.25925926)(t + -4.25925926) = 21.474622773 Calculate the square root of the right side: 4.634071943 Break this problem into two subproblems by setting (t + -4.25925926) equal to 4.634071943 and -4.634071943.Subproblem 1
t + -4.25925926 = 4.634071943 Simplifying t + -4.25925926 = 4.634071943 Reorder the terms: -4.25925926 + t = 4.634071943 Solving -4.25925926 + t = 4.634071943 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.25925926' to each side of the equation. -4.25925926 + 4.25925926 + t = 4.634071943 + 4.25925926 Combine like terms: -4.25925926 + 4.25925926 = 0.00000000 0.00000000 + t = 4.634071943 + 4.25925926 t = 4.634071943 + 4.25925926 Combine like terms: 4.634071943 + 4.25925926 = 8.893331203 t = 8.893331203 Simplifying t = 8.893331203Subproblem 2
t + -4.25925926 = -4.634071943 Simplifying t + -4.25925926 = -4.634071943 Reorder the terms: -4.25925926 + t = -4.634071943 Solving -4.25925926 + t = -4.634071943 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.25925926' to each side of the equation. -4.25925926 + 4.25925926 + t = -4.634071943 + 4.25925926 Combine like terms: -4.25925926 + 4.25925926 = 0.00000000 0.00000000 + t = -4.634071943 + 4.25925926 t = -4.634071943 + 4.25925926 Combine like terms: -4.634071943 + 4.25925926 = -0.374812683 t = -0.374812683 Simplifying t = -0.374812683Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.893331203, -0.374812683}
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