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Simplifying 1.9 = 0.0756t2 + -0.025t Reorder the terms: 1.9 = -0.025t + 0.0756t2 Solving 1.9 = -0.025t + 0.0756t2 Solving for variable 't'. Reorder the terms: 1.9 + 0.025t + -0.0756t2 = -0.025t + 0.025t + 0.0756t2 + -0.0756t2 Combine like terms: -0.025t + 0.025t = 0.000 1.9 + 0.025t + -0.0756t2 = 0.000 + 0.0756t2 + -0.0756t2 1.9 + 0.025t + -0.0756t2 = 0.0756t2 + -0.0756t2 Combine like terms: 0.0756t2 + -0.0756t2 = 0.0000 1.9 + 0.025t + -0.0756t2 = 0.0000 Begin completing the square. Divide all terms by -0.0756 the coefficient of the squared term: Divide each side by '-0.0756'. -25.13227513 + -0.3306878307t + t2 = 0 Move the constant term to the right: Add '25.13227513' to each side of the equation. -25.13227513 + -0.3306878307t + 25.13227513 + t2 = 0 + 25.13227513 Reorder the terms: -25.13227513 + 25.13227513 + -0.3306878307t + t2 = 0 + 25.13227513 Combine like terms: -25.13227513 + 25.13227513 = 0.00000000 0.00000000 + -0.3306878307t + t2 = 0 + 25.13227513 -0.3306878307t + t2 = 0 + 25.13227513 Combine like terms: 0 + 25.13227513 = 25.13227513 -0.3306878307t + t2 = 25.13227513 The t term is -0.3306878307t. Take half its coefficient (-0.1653439154). Square it (0.02733861036) and add it to both sides. Add '0.02733861036' to each side of the equation. -0.3306878307t + 0.02733861036 + t2 = 25.13227513 + 0.02733861036 Reorder the terms: 0.02733861036 + -0.3306878307t + t2 = 25.13227513 + 0.02733861036 Combine like terms: 25.13227513 + 0.02733861036 = 25.15961374036 0.02733861036 + -0.3306878307t + t2 = 25.15961374036 Factor a perfect square on the left side: (t + -0.1653439154)(t + -0.1653439154) = 25.15961374036 Calculate the square root of the right side: 5.015935978 Break this problem into two subproblems by setting (t + -0.1653439154) equal to 5.015935978 and -5.015935978.Subproblem 1
t + -0.1653439154 = 5.015935978 Simplifying t + -0.1653439154 = 5.015935978 Reorder the terms: -0.1653439154 + t = 5.015935978 Solving -0.1653439154 + t = 5.015935978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1653439154' to each side of the equation. -0.1653439154 + 0.1653439154 + t = 5.015935978 + 0.1653439154 Combine like terms: -0.1653439154 + 0.1653439154 = 0.0000000000 0.0000000000 + t = 5.015935978 + 0.1653439154 t = 5.015935978 + 0.1653439154 Combine like terms: 5.015935978 + 0.1653439154 = 5.1812798934 t = 5.1812798934 Simplifying t = 5.1812798934Subproblem 2
t + -0.1653439154 = -5.015935978 Simplifying t + -0.1653439154 = -5.015935978 Reorder the terms: -0.1653439154 + t = -5.015935978 Solving -0.1653439154 + t = -5.015935978 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1653439154' to each side of the equation. -0.1653439154 + 0.1653439154 + t = -5.015935978 + 0.1653439154 Combine like terms: -0.1653439154 + 0.1653439154 = 0.0000000000 0.0000000000 + t = -5.015935978 + 0.1653439154 t = -5.015935978 + 0.1653439154 Combine like terms: -5.015935978 + 0.1653439154 = -4.8505920626 t = -4.8505920626 Simplifying t = -4.8505920626Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.1812798934, -4.8505920626}
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