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Simplifying 0 = 16x2 + 11x + -14 Reorder the terms: 0 = -14 + 11x + 16x2 Solving 0 = -14 + 11x + 16x2 Solving for variable 'x'. Combine like terms: 0 + 14 = 14 14 + -11x + -16x2 = -14 + 11x + 16x2 + 14 + -11x + -16x2 Reorder the terms: 14 + -11x + -16x2 = -14 + 14 + 11x + -11x + 16x2 + -16x2 Combine like terms: -14 + 14 = 0 14 + -11x + -16x2 = 0 + 11x + -11x + 16x2 + -16x2 14 + -11x + -16x2 = 11x + -11x + 16x2 + -16x2 Combine like terms: 11x + -11x = 0 14 + -11x + -16x2 = 0 + 16x2 + -16x2 14 + -11x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 14 + -11x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.875 + 0.6875x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 0.6875x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 0.6875x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 0.6875x + x2 = 0 + 0.875 0.6875x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 0.6875x + x2 = 0.875 The x term is 0.6875x. Take half its coefficient (0.34375). Square it (0.1181640625) and add it to both sides. Add '0.1181640625' to each side of the equation. 0.6875x + 0.1181640625 + x2 = 0.875 + 0.1181640625 Reorder the terms: 0.1181640625 + 0.6875x + x2 = 0.875 + 0.1181640625 Combine like terms: 0.875 + 0.1181640625 = 0.9931640625 0.1181640625 + 0.6875x + x2 = 0.9931640625 Factor a perfect square on the left side: (x + 0.34375)(x + 0.34375) = 0.9931640625 Calculate the square root of the right side: 0.99657617 Break this problem into two subproblems by setting (x + 0.34375) equal to 0.99657617 and -0.99657617.Subproblem 1
x + 0.34375 = 0.99657617 Simplifying x + 0.34375 = 0.99657617 Reorder the terms: 0.34375 + x = 0.99657617 Solving 0.34375 + x = 0.99657617 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.34375' to each side of the equation. 0.34375 + -0.34375 + x = 0.99657617 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + x = 0.99657617 + -0.34375 x = 0.99657617 + -0.34375 Combine like terms: 0.99657617 + -0.34375 = 0.65282617 x = 0.65282617 Simplifying x = 0.65282617Subproblem 2
x + 0.34375 = -0.99657617 Simplifying x + 0.34375 = -0.99657617 Reorder the terms: 0.34375 + x = -0.99657617 Solving 0.34375 + x = -0.99657617 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.34375' to each side of the equation. 0.34375 + -0.34375 + x = -0.99657617 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + x = -0.99657617 + -0.34375 x = -0.99657617 + -0.34375 Combine like terms: -0.99657617 + -0.34375 = -1.34032617 x = -1.34032617 Simplifying x = -1.34032617Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.65282617, -1.34032617}
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