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Simplifying (4x * 4x) + 11x + -69 = 0 Reorder the terms for easier multiplication: (4 * 4x * x) + 11x + -69 = 0 Multiply 4 * 4 (16x * x) + 11x + -69 = 0 Multiply x * x (16x2) + 11x + -69 = 0 Reorder the terms: -69 + 11x + (16x2) = 0 Solving -69 + 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'. -4.3125 + 0.6875x + x2 = 0 Move the constant term to the right: Add '4.3125' to each side of the equation. -4.3125 + 0.6875x + 4.3125 + x2 = 0 + 4.3125 Reorder the terms: -4.3125 + 4.3125 + 0.6875x + x2 = 0 + 4.3125 Combine like terms: -4.3125 + 4.3125 = 0.0000 0.0000 + 0.6875x + x2 = 0 + 4.3125 0.6875x + x2 = 0 + 4.3125 Combine like terms: 0 + 4.3125 = 4.3125 0.6875x + x2 = 4.3125 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 = 4.3125 + 0.1181640625 Reorder the terms: 0.1181640625 + 0.6875x + x2 = 4.3125 + 0.1181640625 Combine like terms: 4.3125 + 0.1181640625 = 4.4306640625 0.1181640625 + 0.6875x + x2 = 4.4306640625 Factor a perfect square on the left side: ((x) + 0.34375)((x) + 0.34375) = 4.4306640625 Calculate the square root of the right side: 2.104914265 Break this problem into two subproblems by setting ((x) + 0.34375) equal to 2.104914265 and -2.104914265.Subproblem 1
(x) + 0.34375 = 2.104914265 Simplifying (x) + 0.34375 = 2.104914265 x + 0.34375 = 2.104914265 Reorder the terms: 0.34375 + x = 2.104914265 Solving 0.34375 + x = 2.104914265 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 = 2.104914265 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + x = 2.104914265 + -0.34375 x = 2.104914265 + -0.34375 Combine like terms: 2.104914265 + -0.34375 = 1.761164265 x = 1.761164265 Simplifying x = 1.761164265Subproblem 2
(x) + 0.34375 = -2.104914265 Simplifying (x) + 0.34375 = -2.104914265 x + 0.34375 = -2.104914265 Reorder the terms: 0.34375 + x = -2.104914265 Solving 0.34375 + x = -2.104914265 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 = -2.104914265 + -0.34375 Combine like terms: 0.34375 + -0.34375 = 0.00000 0.00000 + x = -2.104914265 + -0.34375 x = -2.104914265 + -0.34375 Combine like terms: -2.104914265 + -0.34375 = -2.448664265 x = -2.448664265 Simplifying x = -2.448664265Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.761164265, -2.448664265}
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