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Simplifying -16x2 + 133x = 43.5 Reorder the terms: 133x + -16x2 = 43.5 Solving 133x + -16x2 = 43.5 Solving for variable 'x'. Reorder the terms: -43.5 + 133x + -16x2 = 43.5 + -43.5 Combine like terms: 43.5 + -43.5 = 0.0 -43.5 + 133x + -16x2 = 0.0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. 2.71875 + -8.3125x + x2 = 0.0 Move the constant term to the right: Add '-2.71875' to each side of the equation. 2.71875 + -8.3125x + -2.71875 + x2 = 0.0 + -2.71875 Reorder the terms: 2.71875 + -2.71875 + -8.3125x + x2 = 0.0 + -2.71875 Combine like terms: 2.71875 + -2.71875 = 0.00000 0.00000 + -8.3125x + x2 = 0.0 + -2.71875 -8.3125x + x2 = 0.0 + -2.71875 Combine like terms: 0.0 + -2.71875 = -2.71875 -8.3125x + x2 = -2.71875 The x term is -8.3125x. Take half its coefficient (-4.15625). Square it (17.27441406) and add it to both sides. Add '17.27441406' to each side of the equation. -8.3125x + 17.27441406 + x2 = -2.71875 + 17.27441406 Reorder the terms: 17.27441406 + -8.3125x + x2 = -2.71875 + 17.27441406 Combine like terms: -2.71875 + 17.27441406 = 14.55566406 17.27441406 + -8.3125x + x2 = 14.55566406 Factor a perfect square on the left side: (x + -4.15625)(x + -4.15625) = 14.55566406 Calculate the square root of the right side: 3.815188601 Break this problem into two subproblems by setting (x + -4.15625) equal to 3.815188601 and -3.815188601.Subproblem 1
x + -4.15625 = 3.815188601 Simplifying x + -4.15625 = 3.815188601 Reorder the terms: -4.15625 + x = 3.815188601 Solving -4.15625 + x = 3.815188601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.15625' to each side of the equation. -4.15625 + 4.15625 + x = 3.815188601 + 4.15625 Combine like terms: -4.15625 + 4.15625 = 0.00000 0.00000 + x = 3.815188601 + 4.15625 x = 3.815188601 + 4.15625 Combine like terms: 3.815188601 + 4.15625 = 7.971438601 x = 7.971438601 Simplifying x = 7.971438601Subproblem 2
x + -4.15625 = -3.815188601 Simplifying x + -4.15625 = -3.815188601 Reorder the terms: -4.15625 + x = -3.815188601 Solving -4.15625 + x = -3.815188601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.15625' to each side of the equation. -4.15625 + 4.15625 + x = -3.815188601 + 4.15625 Combine like terms: -4.15625 + 4.15625 = 0.00000 0.00000 + x = -3.815188601 + 4.15625 x = -3.815188601 + 4.15625 Combine like terms: -3.815188601 + 4.15625 = 0.341061399 x = 0.341061399 Simplifying x = 0.341061399Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.971438601, 0.341061399}
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