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Simplifying 15t2 + -11t + -12 = 9 Reorder the terms: -12 + -11t + 15t2 = 9 Solving -12 + -11t + 15t2 = 9 Solving for variable 't'. Reorder the terms: -12 + -9 + -11t + 15t2 = 9 + -9 Combine like terms: -12 + -9 = -21 -21 + -11t + 15t2 = 9 + -9 Combine like terms: 9 + -9 = 0 -21 + -11t + 15t2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.4 + -0.7333333333t + t2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + -0.7333333333t + 1.4 + t2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + -0.7333333333t + t2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + -0.7333333333t + t2 = 0 + 1.4 -0.7333333333t + t2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 -0.7333333333t + t2 = 1.4 The t term is -0.7333333333t. Take half its coefficient (-0.3666666667). Square it (0.1344444445) and add it to both sides. Add '0.1344444445' to each side of the equation. -0.7333333333t + 0.1344444445 + t2 = 1.4 + 0.1344444445 Reorder the terms: 0.1344444445 + -0.7333333333t + t2 = 1.4 + 0.1344444445 Combine like terms: 1.4 + 0.1344444445 = 1.5344444445 0.1344444445 + -0.7333333333t + t2 = 1.5344444445 Factor a perfect square on the left side: (t + -0.3666666667)(t + -0.3666666667) = 1.5344444445 Calculate the square root of the right side: 1.238726945 Break this problem into two subproblems by setting (t + -0.3666666667) equal to 1.238726945 and -1.238726945.Subproblem 1
t + -0.3666666667 = 1.238726945 Simplifying t + -0.3666666667 = 1.238726945 Reorder the terms: -0.3666666667 + t = 1.238726945 Solving -0.3666666667 + t = 1.238726945 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3666666667' to each side of the equation. -0.3666666667 + 0.3666666667 + t = 1.238726945 + 0.3666666667 Combine like terms: -0.3666666667 + 0.3666666667 = 0.0000000000 0.0000000000 + t = 1.238726945 + 0.3666666667 t = 1.238726945 + 0.3666666667 Combine like terms: 1.238726945 + 0.3666666667 = 1.6053936117 t = 1.6053936117 Simplifying t = 1.6053936117Subproblem 2
t + -0.3666666667 = -1.238726945 Simplifying t + -0.3666666667 = -1.238726945 Reorder the terms: -0.3666666667 + t = -1.238726945 Solving -0.3666666667 + t = -1.238726945 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3666666667' to each side of the equation. -0.3666666667 + 0.3666666667 + t = -1.238726945 + 0.3666666667 Combine like terms: -0.3666666667 + 0.3666666667 = 0.0000000000 0.0000000000 + t = -1.238726945 + 0.3666666667 t = -1.238726945 + 0.3666666667 Combine like terms: -1.238726945 + 0.3666666667 = -0.8720602783 t = -0.8720602783 Simplifying t = -0.8720602783Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.6053936117, -0.8720602783}
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