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Simplifying 4.9t2 + -6.9t + -1.5 = 0 Reorder the terms: -1.5 + -6.9t + 4.9t2 = 0 Solving -1.5 + -6.9t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -0.306122449 + -1.408163265t + t2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -1.408163265t + 0.306122449 + t2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -1.408163265t + t2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -1.408163265t + t2 = 0 + 0.306122449 -1.408163265t + t2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -1.408163265t + t2 = 0.306122449 The t term is -1.408163265t. Take half its coefficient (-0.7040816325). Square it (0.4957309452) and add it to both sides. Add '0.4957309452' to each side of the equation. -1.408163265t + 0.4957309452 + t2 = 0.306122449 + 0.4957309452 Reorder the terms: 0.4957309452 + -1.408163265t + t2 = 0.306122449 + 0.4957309452 Combine like terms: 0.306122449 + 0.4957309452 = 0.8018533942 0.4957309452 + -1.408163265t + t2 = 0.8018533942 Factor a perfect square on the left side: (t + -0.7040816325)(t + -0.7040816325) = 0.8018533942 Calculate the square root of the right side: 0.89546267 Break this problem into two subproblems by setting (t + -0.7040816325) equal to 0.89546267 and -0.89546267.Subproblem 1
t + -0.7040816325 = 0.89546267 Simplifying t + -0.7040816325 = 0.89546267 Reorder the terms: -0.7040816325 + t = 0.89546267 Solving -0.7040816325 + t = 0.89546267 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7040816325' to each side of the equation. -0.7040816325 + 0.7040816325 + t = 0.89546267 + 0.7040816325 Combine like terms: -0.7040816325 + 0.7040816325 = 0.0000000000 0.0000000000 + t = 0.89546267 + 0.7040816325 t = 0.89546267 + 0.7040816325 Combine like terms: 0.89546267 + 0.7040816325 = 1.5995443025 t = 1.5995443025 Simplifying t = 1.5995443025Subproblem 2
t + -0.7040816325 = -0.89546267 Simplifying t + -0.7040816325 = -0.89546267 Reorder the terms: -0.7040816325 + t = -0.89546267 Solving -0.7040816325 + t = -0.89546267 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.7040816325' to each side of the equation. -0.7040816325 + 0.7040816325 + t = -0.89546267 + 0.7040816325 Combine like terms: -0.7040816325 + 0.7040816325 = 0.0000000000 0.0000000000 + t = -0.89546267 + 0.7040816325 t = -0.89546267 + 0.7040816325 Combine like terms: -0.89546267 + 0.7040816325 = -0.1913810375 t = -0.1913810375 Simplifying t = -0.1913810375Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.5995443025, -0.1913810375}
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