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Simplifying -4.9t2 + -2.3t + 5 = 0 Reorder the terms: 5 + -2.3t + -4.9t2 = 0 Solving 5 + -2.3t + -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'. -1.020408163 + 0.4693877551t + t2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + 0.4693877551t + 1.020408163 + t2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + 0.4693877551t + t2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + 0.4693877551t + t2 = 0 + 1.020408163 0.4693877551t + t2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 0.4693877551t + t2 = 1.020408163 The t term is 0.4693877551t. Take half its coefficient (0.2346938776). Square it (0.05508121618) and add it to both sides. Add '0.05508121618' to each side of the equation. 0.4693877551t + 0.05508121618 + t2 = 1.020408163 + 0.05508121618 Reorder the terms: 0.05508121618 + 0.4693877551t + t2 = 1.020408163 + 0.05508121618 Combine like terms: 1.020408163 + 0.05508121618 = 1.07548937918 0.05508121618 + 0.4693877551t + t2 = 1.07548937918 Factor a perfect square on the left side: (t + 0.2346938776)(t + 0.2346938776) = 1.07548937918 Calculate the square root of the right side: 1.03705804 Break this problem into two subproblems by setting (t + 0.2346938776) equal to 1.03705804 and -1.03705804.Subproblem 1
t + 0.2346938776 = 1.03705804 Simplifying t + 0.2346938776 = 1.03705804 Reorder the terms: 0.2346938776 + t = 1.03705804 Solving 0.2346938776 + t = 1.03705804 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2346938776' to each side of the equation. 0.2346938776 + -0.2346938776 + t = 1.03705804 + -0.2346938776 Combine like terms: 0.2346938776 + -0.2346938776 = 0.0000000000 0.0000000000 + t = 1.03705804 + -0.2346938776 t = 1.03705804 + -0.2346938776 Combine like terms: 1.03705804 + -0.2346938776 = 0.8023641624 t = 0.8023641624 Simplifying t = 0.8023641624Subproblem 2
t + 0.2346938776 = -1.03705804 Simplifying t + 0.2346938776 = -1.03705804 Reorder the terms: 0.2346938776 + t = -1.03705804 Solving 0.2346938776 + t = -1.03705804 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.2346938776' to each side of the equation. 0.2346938776 + -0.2346938776 + t = -1.03705804 + -0.2346938776 Combine like terms: 0.2346938776 + -0.2346938776 = 0.0000000000 0.0000000000 + t = -1.03705804 + -0.2346938776 t = -1.03705804 + -0.2346938776 Combine like terms: -1.03705804 + -0.2346938776 = -1.2717519176 t = -1.2717519176 Simplifying t = -1.2717519176Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.8023641624, -1.2717519176}
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