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Simplifying 63t2 + -75t + -52 = 0 Reorder the terms: -52 + -75t + 63t2 = 0 Solving -52 + -75t + 63t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 63 the coefficient of the squared term: Divide each side by '63'. -0.8253968254 + -1.19047619t + t2 = 0 Move the constant term to the right: Add '0.8253968254' to each side of the equation. -0.8253968254 + -1.19047619t + 0.8253968254 + t2 = 0 + 0.8253968254 Reorder the terms: -0.8253968254 + 0.8253968254 + -1.19047619t + t2 = 0 + 0.8253968254 Combine like terms: -0.8253968254 + 0.8253968254 = 0.0000000000 0.0000000000 + -1.19047619t + t2 = 0 + 0.8253968254 -1.19047619t + t2 = 0 + 0.8253968254 Combine like terms: 0 + 0.8253968254 = 0.8253968254 -1.19047619t + t2 = 0.8253968254 The t term is -1.19047619t. Take half its coefficient (-0.595238095). Square it (0.3543083897) and add it to both sides. Add '0.3543083897' to each side of the equation. -1.19047619t + 0.3543083897 + t2 = 0.8253968254 + 0.3543083897 Reorder the terms: 0.3543083897 + -1.19047619t + t2 = 0.8253968254 + 0.3543083897 Combine like terms: 0.8253968254 + 0.3543083897 = 1.1797052151 0.3543083897 + -1.19047619t + t2 = 1.1797052151 Factor a perfect square on the left side: (t + -0.595238095)(t + -0.595238095) = 1.1797052151 Calculate the square root of the right side: 1.086142355 Break this problem into two subproblems by setting (t + -0.595238095) equal to 1.086142355 and -1.086142355.Subproblem 1
t + -0.595238095 = 1.086142355 Simplifying t + -0.595238095 = 1.086142355 Reorder the terms: -0.595238095 + t = 1.086142355 Solving -0.595238095 + t = 1.086142355 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.595238095' to each side of the equation. -0.595238095 + 0.595238095 + t = 1.086142355 + 0.595238095 Combine like terms: -0.595238095 + 0.595238095 = 0.000000000 0.000000000 + t = 1.086142355 + 0.595238095 t = 1.086142355 + 0.595238095 Combine like terms: 1.086142355 + 0.595238095 = 1.68138045 t = 1.68138045 Simplifying t = 1.68138045Subproblem 2
t + -0.595238095 = -1.086142355 Simplifying t + -0.595238095 = -1.086142355 Reorder the terms: -0.595238095 + t = -1.086142355 Solving -0.595238095 + t = -1.086142355 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.595238095' to each side of the equation. -0.595238095 + 0.595238095 + t = -1.086142355 + 0.595238095 Combine like terms: -0.595238095 + 0.595238095 = 0.000000000 0.000000000 + t = -1.086142355 + 0.595238095 t = -1.086142355 + 0.595238095 Combine like terms: -1.086142355 + 0.595238095 = -0.49090426 t = -0.49090426 Simplifying t = -0.49090426Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.68138045, -0.49090426}
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