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Simplifying 16x2 + -11x + -25 = 0 Reorder the terms: -25 + -11x + 16x2 = 0 Solving -25 + -11x + 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'. -1.5625 + -0.6875x + x2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + -0.6875x + 1.5625 + x2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + -0.6875x + x2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + -0.6875x + x2 = 0 + 1.5625 -0.6875x + x2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 -0.6875x + x2 = 1.5625 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 = 1.5625 + 0.1181640625 Reorder the terms: 0.1181640625 + -0.6875x + x2 = 1.5625 + 0.1181640625 Combine like terms: 1.5625 + 0.1181640625 = 1.6806640625 0.1181640625 + -0.6875x + x2 = 1.6806640625 Factor a perfect square on the left side: (x + -0.34375)(x + -0.34375) = 1.6806640625 Calculate the square root of the right side: 1.296404282 Break this problem into two subproblems by setting (x + -0.34375) equal to 1.296404282 and -1.296404282.Subproblem 1
x + -0.34375 = 1.296404282 Simplifying x + -0.34375 = 1.296404282 Reorder the terms: -0.34375 + x = 1.296404282 Solving -0.34375 + x = 1.296404282 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 = 1.296404282 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + x = 1.296404282 + 0.34375 x = 1.296404282 + 0.34375 Combine like terms: 1.296404282 + 0.34375 = 1.640154282 x = 1.640154282 Simplifying x = 1.640154282Subproblem 2
x + -0.34375 = -1.296404282 Simplifying x + -0.34375 = -1.296404282 Reorder the terms: -0.34375 + x = -1.296404282 Solving -0.34375 + x = -1.296404282 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 = -1.296404282 + 0.34375 Combine like terms: -0.34375 + 0.34375 = 0.00000 0.00000 + x = -1.296404282 + 0.34375 x = -1.296404282 + 0.34375 Combine like terms: -1.296404282 + 0.34375 = -0.952654282 x = -0.952654282 Simplifying x = -0.952654282Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.640154282, -0.952654282}
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