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Simplifying 10t2 + -27t + -5 = 0 Reorder the terms: -5 + -27t + 10t2 = 0 Solving -5 + -27t + 10t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.5 + -2.7t + t2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.7t + 0.5 + t2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.7t + t2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.7t + t2 = 0 + 0.5 -2.7t + t2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2.7t + t2 = 0.5 The t term is -2.7t. Take half its coefficient (-1.35). Square it (1.8225) and add it to both sides. Add '1.8225' to each side of the equation. -2.7t + 1.8225 + t2 = 0.5 + 1.8225 Reorder the terms: 1.8225 + -2.7t + t2 = 0.5 + 1.8225 Combine like terms: 0.5 + 1.8225 = 2.3225 1.8225 + -2.7t + t2 = 2.3225 Factor a perfect square on the left side: (t + -1.35)(t + -1.35) = 2.3225 Calculate the square root of the right side: 1.523975065 Break this problem into two subproblems by setting (t + -1.35) equal to 1.523975065 and -1.523975065.Subproblem 1
t + -1.35 = 1.523975065 Simplifying t + -1.35 = 1.523975065 Reorder the terms: -1.35 + t = 1.523975065 Solving -1.35 + t = 1.523975065 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + t = 1.523975065 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + t = 1.523975065 + 1.35 t = 1.523975065 + 1.35 Combine like terms: 1.523975065 + 1.35 = 2.873975065 t = 2.873975065 Simplifying t = 2.873975065Subproblem 2
t + -1.35 = -1.523975065 Simplifying t + -1.35 = -1.523975065 Reorder the terms: -1.35 + t = -1.523975065 Solving -1.35 + t = -1.523975065 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.35' to each side of the equation. -1.35 + 1.35 + t = -1.523975065 + 1.35 Combine like terms: -1.35 + 1.35 = 0.00 0.00 + t = -1.523975065 + 1.35 t = -1.523975065 + 1.35 Combine like terms: -1.523975065 + 1.35 = -0.173975065 t = -0.173975065 Simplifying t = -0.173975065Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.873975065, -0.173975065}
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