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Simplifying 15t2 = 2t + 63 Reorder the terms: 15t2 = 63 + 2t Solving 15t2 = 63 + 2t Solving for variable 't'. Reorder the terms: -63 + -2t + 15t2 = 63 + 2t + -63 + -2t Reorder the terms: -63 + -2t + 15t2 = 63 + -63 + 2t + -2t Combine like terms: 63 + -63 = 0 -63 + -2t + 15t2 = 0 + 2t + -2t -63 + -2t + 15t2 = 2t + -2t Combine like terms: 2t + -2t = 0 -63 + -2t + 15t2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -4.2 + -0.1333333333t + t2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + -0.1333333333t + 4.2 + t2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + -0.1333333333t + t2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + -0.1333333333t + t2 = 0 + 4.2 -0.1333333333t + t2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 -0.1333333333t + t2 = 4.2 The t term is -0.1333333333t. Take half its coefficient (-0.06666666665). Square it (0.004444444442) and add it to both sides. Add '0.004444444442' to each side of the equation. -0.1333333333t + 0.004444444442 + t2 = 4.2 + 0.004444444442 Reorder the terms: 0.004444444442 + -0.1333333333t + t2 = 4.2 + 0.004444444442 Combine like terms: 4.2 + 0.004444444442 = 4.204444444442 0.004444444442 + -0.1333333333t + t2 = 4.204444444442 Factor a perfect square on the left side: (t + -0.06666666665)(t + -0.06666666665) = 4.204444444442 Calculate the square root of the right side: 2.0504742 Break this problem into two subproblems by setting (t + -0.06666666665) equal to 2.0504742 and -2.0504742.Subproblem 1
t + -0.06666666665 = 2.0504742 Simplifying t + -0.06666666665 = 2.0504742 Reorder the terms: -0.06666666665 + t = 2.0504742 Solving -0.06666666665 + t = 2.0504742 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + t = 2.0504742 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + t = 2.0504742 + 0.06666666665 t = 2.0504742 + 0.06666666665 Combine like terms: 2.0504742 + 0.06666666665 = 2.11714086665 t = 2.11714086665 Simplifying t = 2.11714086665Subproblem 2
t + -0.06666666665 = -2.0504742 Simplifying t + -0.06666666665 = -2.0504742 Reorder the terms: -0.06666666665 + t = -2.0504742 Solving -0.06666666665 + t = -2.0504742 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.06666666665' to each side of the equation. -0.06666666665 + 0.06666666665 + t = -2.0504742 + 0.06666666665 Combine like terms: -0.06666666665 + 0.06666666665 = 0.00000000000 0.00000000000 + t = -2.0504742 + 0.06666666665 t = -2.0504742 + 0.06666666665 Combine like terms: -2.0504742 + 0.06666666665 = -1.98380753335 t = -1.98380753335 Simplifying t = -1.98380753335Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.11714086665, -1.98380753335}
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