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Simplifying 4.9t2 + -23t + -15 = 0 Reorder the terms: -15 + -23t + 4.9t2 = 0 Solving -15 + -23t + 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'. -3.06122449 + -4.693877551t + t2 = 0 Move the constant term to the right: Add '3.06122449' to each side of the equation. -3.06122449 + -4.693877551t + 3.06122449 + t2 = 0 + 3.06122449 Reorder the terms: -3.06122449 + 3.06122449 + -4.693877551t + t2 = 0 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + -4.693877551t + t2 = 0 + 3.06122449 -4.693877551t + t2 = 0 + 3.06122449 Combine like terms: 0 + 3.06122449 = 3.06122449 -4.693877551t + t2 = 3.06122449 The t term is -4.693877551t. Take half its coefficient (-2.346938776). Square it (5.508121618) and add it to both sides. Add '5.508121618' to each side of the equation. -4.693877551t + 5.508121618 + t2 = 3.06122449 + 5.508121618 Reorder the terms: 5.508121618 + -4.693877551t + t2 = 3.06122449 + 5.508121618 Combine like terms: 3.06122449 + 5.508121618 = 8.569346108 5.508121618 + -4.693877551t + t2 = 8.569346108 Factor a perfect square on the left side: (t + -2.346938776)(t + -2.346938776) = 8.569346108 Calculate the square root of the right side: 2.927344549 Break this problem into two subproblems by setting (t + -2.346938776) equal to 2.927344549 and -2.927344549.Subproblem 1
t + -2.346938776 = 2.927344549 Simplifying t + -2.346938776 = 2.927344549 Reorder the terms: -2.346938776 + t = 2.927344549 Solving -2.346938776 + t = 2.927344549 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.346938776' to each side of the equation. -2.346938776 + 2.346938776 + t = 2.927344549 + 2.346938776 Combine like terms: -2.346938776 + 2.346938776 = 0.000000000 0.000000000 + t = 2.927344549 + 2.346938776 t = 2.927344549 + 2.346938776 Combine like terms: 2.927344549 + 2.346938776 = 5.274283325 t = 5.274283325 Simplifying t = 5.274283325Subproblem 2
t + -2.346938776 = -2.927344549 Simplifying t + -2.346938776 = -2.927344549 Reorder the terms: -2.346938776 + t = -2.927344549 Solving -2.346938776 + t = -2.927344549 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.346938776' to each side of the equation. -2.346938776 + 2.346938776 + t = -2.927344549 + 2.346938776 Combine like terms: -2.346938776 + 2.346938776 = 0.000000000 0.000000000 + t = -2.927344549 + 2.346938776 t = -2.927344549 + 2.346938776 Combine like terms: -2.927344549 + 2.346938776 = -0.580405773 t = -0.580405773 Simplifying t = -0.580405773Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.274283325, -0.580405773}
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