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Simplifying 4t2 + -5t + -75 = 304 Reorder the terms: -75 + -5t + 4t2 = 304 Solving -75 + -5t + 4t2 = 304 Solving for variable 't'. Reorder the terms: -75 + -304 + -5t + 4t2 = 304 + -304 Combine like terms: -75 + -304 = -379 -379 + -5t + 4t2 = 304 + -304 Combine like terms: 304 + -304 = 0 -379 + -5t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -94.75 + -1.25t + t2 = 0 Move the constant term to the right: Add '94.75' to each side of the equation. -94.75 + -1.25t + 94.75 + t2 = 0 + 94.75 Reorder the terms: -94.75 + 94.75 + -1.25t + t2 = 0 + 94.75 Combine like terms: -94.75 + 94.75 = 0.00 0.00 + -1.25t + t2 = 0 + 94.75 -1.25t + t2 = 0 + 94.75 Combine like terms: 0 + 94.75 = 94.75 -1.25t + t2 = 94.75 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 = 94.75 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = 94.75 + 0.390625 Combine like terms: 94.75 + 0.390625 = 95.140625 0.390625 + -1.25t + t2 = 95.140625 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = 95.140625 Calculate the square root of the right side: 9.754005587 Break this problem into two subproblems by setting (t + -0.625) equal to 9.754005587 and -9.754005587.Subproblem 1
t + -0.625 = 9.754005587 Simplifying t + -0.625 = 9.754005587 Reorder the terms: -0.625 + t = 9.754005587 Solving -0.625 + t = 9.754005587 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 = 9.754005587 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = 9.754005587 + 0.625 t = 9.754005587 + 0.625 Combine like terms: 9.754005587 + 0.625 = 10.379005587 t = 10.379005587 Simplifying t = 10.379005587Subproblem 2
t + -0.625 = -9.754005587 Simplifying t + -0.625 = -9.754005587 Reorder the terms: -0.625 + t = -9.754005587 Solving -0.625 + t = -9.754005587 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 = -9.754005587 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = -9.754005587 + 0.625 t = -9.754005587 + 0.625 Combine like terms: -9.754005587 + 0.625 = -9.129005587 t = -9.129005587 Simplifying t = -9.129005587Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.379005587, -9.129005587}
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