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Simplifying 4t2 + -5t + -12 = 0 Reorder the terms: -12 + -5t + 4t2 = 0 Solving -12 + -5t + 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'. -3 + -1.25t + t2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1.25t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + -1.25t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1.25t + t2 = 0 + 3 -1.25t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1.25t + t2 = 3 The t term is -1.25t. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25t + 0.390625 + t2 = 3 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = 3 + 0.390625 Combine like terms: 3 + 0.390625 = 3.390625 0.390625 + -1.25t + t2 = 3.390625 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = 3.390625 Calculate the square root of the right side: 1.841364983 Break this problem into two subproblems by setting (t + -0.625) equal to 1.841364983 and -1.841364983.Subproblem 1
t + -0.625 = 1.841364983 Simplifying t + -0.625 = 1.841364983 Reorder the terms: -0.625 + t = 1.841364983 Solving -0.625 + t = 1.841364983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = 1.841364983 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = 1.841364983 + 0.625 t = 1.841364983 + 0.625 Combine like terms: 1.841364983 + 0.625 = 2.466364983 t = 2.466364983 Simplifying t = 2.466364983Subproblem 2
t + -0.625 = -1.841364983 Simplifying t + -0.625 = -1.841364983 Reorder the terms: -0.625 + t = -1.841364983 Solving -0.625 + t = -1.841364983 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = -1.841364983 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = -1.841364983 + 0.625 t = -1.841364983 + 0.625 Combine like terms: -1.841364983 + 0.625 = -1.216364983 t = -1.216364983 Simplifying t = -1.216364983Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.466364983, -1.216364983}
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