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Simplifying -4.9t2 + 6.5t + 7 = 0 Reorder the terms: 7 + 6.5t + -4.9t2 = 0 Solving 7 + 6.5t + -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'. -1.428571429 + -1.326530612t + t2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -1.326530612t + 1.428571429 + t2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -1.326530612t + t2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -1.326530612t + t2 = 0 + 1.428571429 -1.326530612t + t2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -1.326530612t + t2 = 1.428571429 The t term is -1.326530612t. Take half its coefficient (-0.663265306). Square it (0.4399208661) and add it to both sides. Add '0.4399208661' to each side of the equation. -1.326530612t + 0.4399208661 + t2 = 1.428571429 + 0.4399208661 Reorder the terms: 0.4399208661 + -1.326530612t + t2 = 1.428571429 + 0.4399208661 Combine like terms: 1.428571429 + 0.4399208661 = 1.8684922951 0.4399208661 + -1.326530612t + t2 = 1.8684922951 Factor a perfect square on the left side: (t + -0.663265306)(t + -0.663265306) = 1.8684922951 Calculate the square root of the right side: 1.36692805 Break this problem into two subproblems by setting (t + -0.663265306) equal to 1.36692805 and -1.36692805.Subproblem 1
t + -0.663265306 = 1.36692805 Simplifying t + -0.663265306 = 1.36692805 Reorder the terms: -0.663265306 + t = 1.36692805 Solving -0.663265306 + t = 1.36692805 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.663265306' to each side of the equation. -0.663265306 + 0.663265306 + t = 1.36692805 + 0.663265306 Combine like terms: -0.663265306 + 0.663265306 = 0.000000000 0.000000000 + t = 1.36692805 + 0.663265306 t = 1.36692805 + 0.663265306 Combine like terms: 1.36692805 + 0.663265306 = 2.030193356 t = 2.030193356 Simplifying t = 2.030193356Subproblem 2
t + -0.663265306 = -1.36692805 Simplifying t + -0.663265306 = -1.36692805 Reorder the terms: -0.663265306 + t = -1.36692805 Solving -0.663265306 + t = -1.36692805 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.663265306' to each side of the equation. -0.663265306 + 0.663265306 + t = -1.36692805 + 0.663265306 Combine like terms: -0.663265306 + 0.663265306 = 0.000000000 0.000000000 + t = -1.36692805 + 0.663265306 t = -1.36692805 + 0.663265306 Combine like terms: -1.36692805 + 0.663265306 = -0.703662744 t = -0.703662744 Simplifying t = -0.703662744Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.030193356, -0.703662744}
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