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Simplifying 15t2 + -27t + -25 = 0 Reorder the terms: -25 + -27t + 15t2 = 0 Solving -25 + -27t + 15t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.666666667 + -1.8t + t2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -1.8t + 1.666666667 + t2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -1.8t + t2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -1.8t + t2 = 0 + 1.666666667 -1.8t + t2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -1.8t + t2 = 1.666666667 The t term is -1.8t. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8t + 0.81 + t2 = 1.666666667 + 0.81 Reorder the terms: 0.81 + -1.8t + t2 = 1.666666667 + 0.81 Combine like terms: 1.666666667 + 0.81 = 2.476666667 0.81 + -1.8t + t2 = 2.476666667 Factor a perfect square on the left side: (t + -0.9)(t + -0.9) = 2.476666667 Calculate the square root of the right side: 1.573742885 Break this problem into two subproblems by setting (t + -0.9) equal to 1.573742885 and -1.573742885.Subproblem 1
t + -0.9 = 1.573742885 Simplifying t + -0.9 = 1.573742885 Reorder the terms: -0.9 + t = 1.573742885 Solving -0.9 + t = 1.573742885 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + t = 1.573742885 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + t = 1.573742885 + 0.9 t = 1.573742885 + 0.9 Combine like terms: 1.573742885 + 0.9 = 2.473742885 t = 2.473742885 Simplifying t = 2.473742885Subproblem 2
t + -0.9 = -1.573742885 Simplifying t + -0.9 = -1.573742885 Reorder the terms: -0.9 + t = -1.573742885 Solving -0.9 + t = -1.573742885 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + t = -1.573742885 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + t = -1.573742885 + 0.9 t = -1.573742885 + 0.9 Combine like terms: -1.573742885 + 0.9 = -0.673742885 t = -0.673742885 Simplifying t = -0.673742885Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.473742885, -0.673742885}
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