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Simplifying 16x2 + 150x + -295 = 0 Reorder the terms: -295 + 150x + 16x2 = 0 Solving -295 + 150x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -18.4375 + 9.375x + x2 = 0 Move the constant term to the right: Add '18.4375' to each side of the equation. -18.4375 + 9.375x + 18.4375 + x2 = 0 + 18.4375 Reorder the terms: -18.4375 + 18.4375 + 9.375x + x2 = 0 + 18.4375 Combine like terms: -18.4375 + 18.4375 = 0.0000 0.0000 + 9.375x + x2 = 0 + 18.4375 9.375x + x2 = 0 + 18.4375 Combine like terms: 0 + 18.4375 = 18.4375 9.375x + x2 = 18.4375 The x term is 9.375x. Take half its coefficient (4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. 9.375x + 21.97265625 + x2 = 18.4375 + 21.97265625 Reorder the terms: 21.97265625 + 9.375x + x2 = 18.4375 + 21.97265625 Combine like terms: 18.4375 + 21.97265625 = 40.41015625 21.97265625 + 9.375x + x2 = 40.41015625 Factor a perfect square on the left side: (x + 4.6875)(x + 4.6875) = 40.41015625 Calculate the square root of the right side: 6.35689832 Break this problem into two subproblems by setting (x + 4.6875) equal to 6.35689832 and -6.35689832.Subproblem 1
x + 4.6875 = 6.35689832 Simplifying x + 4.6875 = 6.35689832 Reorder the terms: 4.6875 + x = 6.35689832 Solving 4.6875 + x = 6.35689832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + x = 6.35689832 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + x = 6.35689832 + -4.6875 x = 6.35689832 + -4.6875 Combine like terms: 6.35689832 + -4.6875 = 1.66939832 x = 1.66939832 Simplifying x = 1.66939832Subproblem 2
x + 4.6875 = -6.35689832 Simplifying x + 4.6875 = -6.35689832 Reorder the terms: 4.6875 + x = -6.35689832 Solving 4.6875 + x = -6.35689832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + x = -6.35689832 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + x = -6.35689832 + -4.6875 x = -6.35689832 + -4.6875 Combine like terms: -6.35689832 + -4.6875 = -11.04439832 x = -11.04439832 Simplifying x = -11.04439832Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.66939832, -11.04439832}
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