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Simplifying -4.9t2 + 7.22t + 2 = 0 Reorder the terms: 2 + 7.22t + -4.9t2 = 0 Solving 2 + 7.22t + -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'. -0.4081632653 + -1.473469388t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + -1.473469388t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + -1.473469388t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + -1.473469388t + t2 = 0 + 0.4081632653 -1.473469388t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 -1.473469388t + t2 = 0.4081632653 The t term is -1.473469388t. Take half its coefficient (-0.736734694). Square it (0.5427780093) and add it to both sides. Add '0.5427780093' to each side of the equation. -1.473469388t + 0.5427780093 + t2 = 0.4081632653 + 0.5427780093 Reorder the terms: 0.5427780093 + -1.473469388t + t2 = 0.4081632653 + 0.5427780093 Combine like terms: 0.4081632653 + 0.5427780093 = 0.9509412746 0.5427780093 + -1.473469388t + t2 = 0.9509412746 Factor a perfect square on the left side: (t + -0.736734694)(t + -0.736734694) = 0.9509412746 Calculate the square root of the right side: 0.975162179 Break this problem into two subproblems by setting (t + -0.736734694) equal to 0.975162179 and -0.975162179.Subproblem 1
t + -0.736734694 = 0.975162179 Simplifying t + -0.736734694 = 0.975162179 Reorder the terms: -0.736734694 + t = 0.975162179 Solving -0.736734694 + t = 0.975162179 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.736734694' to each side of the equation. -0.736734694 + 0.736734694 + t = 0.975162179 + 0.736734694 Combine like terms: -0.736734694 + 0.736734694 = 0.000000000 0.000000000 + t = 0.975162179 + 0.736734694 t = 0.975162179 + 0.736734694 Combine like terms: 0.975162179 + 0.736734694 = 1.711896873 t = 1.711896873 Simplifying t = 1.711896873Subproblem 2
t + -0.736734694 = -0.975162179 Simplifying t + -0.736734694 = -0.975162179 Reorder the terms: -0.736734694 + t = -0.975162179 Solving -0.736734694 + t = -0.975162179 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.736734694' to each side of the equation. -0.736734694 + 0.736734694 + t = -0.975162179 + 0.736734694 Combine like terms: -0.736734694 + 0.736734694 = 0.000000000 0.000000000 + t = -0.975162179 + 0.736734694 t = -0.975162179 + 0.736734694 Combine like terms: -0.975162179 + 0.736734694 = -0.238427485 t = -0.238427485 Simplifying t = -0.238427485Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.711896873, -0.238427485}
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