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Simplifying 16x2 + 11x + -26 = 0 Reorder the terms: -26 + 11x + 16x2 = 0 Solving -26 + 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'. -1.625 + 0.6875x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 0.6875x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 0.6875x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 0.6875x + x2 = 0 + 1.625 0.6875x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 0.6875x + x2 = 1.625 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 = 1.625 + 0.1181640625 Reorder the terms: 0.1181640625 + 0.6875x + x2 = 1.625 + 0.1181640625 Combine like terms: 1.625 + 0.1181640625 = 1.7431640625 0.1181640625 + 0.6875x + x2 = 1.7431640625 Factor a perfect square on the left side: (x + 0.34375)(x + 0.34375) = 1.7431640625 Calculate the square root of the right side: 1.320289386 Break this problem into two subproblems by setting (x + 0.34375) equal to 1.320289386 and -1.320289386.Subproblem 1
x + 0.34375 = 1.320289386 Simplifying x + 0.34375 = 1.320289386 Reorder the terms: 0.34375 + x = 1.320289386 Solving 0.34375 + x = 1.320289386 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 = 1.320289386 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + x = 1.320289386 + -0.34375 x = 1.320289386 + -0.34375 Combine like terms: 1.320289386 + -0.34375 = 0.976539386 x = 0.976539386 Simplifying x = 0.976539386Subproblem 2
x + 0.34375 = -1.320289386 Simplifying x + 0.34375 = -1.320289386 Reorder the terms: 0.34375 + x = -1.320289386 Solving 0.34375 + x = -1.320289386 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 = -1.320289386 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + x = -1.320289386 + -0.34375 x = -1.320289386 + -0.34375 Combine like terms: -1.320289386 + -0.34375 = -1.664039386 x = -1.664039386 Simplifying x = -1.664039386Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.976539386, -1.664039386}
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