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Simplifying -4t2 + -6t + 11 = 0 Reorder the terms: 11 + -6t + -4t2 = 0 Solving 11 + -6t + -4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -2.75 + 1.5t + t2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 1.5t + 2.75 + t2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 1.5t + t2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 1.5t + t2 = 0 + 2.75 1.5t + t2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 1.5t + t2 = 2.75 The t term is 1.5t. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5t + 0.5625 + t2 = 2.75 + 0.5625 Reorder the terms: 0.5625 + 1.5t + t2 = 2.75 + 0.5625 Combine like terms: 2.75 + 0.5625 = 3.3125 0.5625 + 1.5t + t2 = 3.3125 Factor a perfect square on the left side: (t + 0.75)(t + 0.75) = 3.3125 Calculate the square root of the right side: 1.820027472 Break this problem into two subproblems by setting (t + 0.75) equal to 1.820027472 and -1.820027472.Subproblem 1
t + 0.75 = 1.820027472 Simplifying t + 0.75 = 1.820027472 Reorder the terms: 0.75 + t = 1.820027472 Solving 0.75 + t = 1.820027472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + t = 1.820027472 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = 1.820027472 + -0.75 t = 1.820027472 + -0.75 Combine like terms: 1.820027472 + -0.75 = 1.070027472 t = 1.070027472 Simplifying t = 1.070027472Subproblem 2
t + 0.75 = -1.820027472 Simplifying t + 0.75 = -1.820027472 Reorder the terms: 0.75 + t = -1.820027472 Solving 0.75 + t = -1.820027472 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + t = -1.820027472 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + t = -1.820027472 + -0.75 t = -1.820027472 + -0.75 Combine like terms: -1.820027472 + -0.75 = -2.570027472 t = -2.570027472 Simplifying t = -2.570027472Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.070027472, -2.570027472}
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