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Simplifying x + 1(11x + -55) + 6x(5x) = 0 Reorder the terms: x + 1(-55 + 11x) + 6x(5x) = 0 x + (-55 * 1 + 11x * 1) + 6x(5x) = 0 x + (-55 + 11x) + 6x(5x) = 0 Remove parenthesis around (5x) x + -55 + 11x + 6x * 5x = 0 Reorder the terms for easier multiplication: x + -55 + 11x + 6 * 5x * x = 0 Multiply 6 * 5 x + -55 + 11x + 30x * x = 0 Multiply x * x x + -55 + 11x + 30x2 = 0 Reorder the terms: -55 + x + 11x + 30x2 = 0 Combine like terms: x + 11x = 12x -55 + 12x + 30x2 = 0 Solving -55 + 12x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -1.833333333 + 0.4x + x2 = 0.0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + 0.4x + 1.833333333 + x2 = 0.0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + 0.4x + x2 = 0.0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + 0.4x + x2 = 0.0 + 1.833333333 0.4x + x2 = 0.0 + 1.833333333 Combine like terms: 0.0 + 1.833333333 = 1.833333333 0.4x + x2 = 1.833333333 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 1.833333333 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 1.833333333 + 0.04 Combine like terms: 1.833333333 + 0.04 = 1.873333333 0.04 + 0.4x + x2 = 1.873333333 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 1.873333333 Calculate the square root of the right side: 1.368697678 Break this problem into two subproblems by setting (x + 0.2) equal to 1.368697678 and -1.368697678.Subproblem 1
x + 0.2 = 1.368697678 Simplifying x + 0.2 = 1.368697678 Reorder the terms: 0.2 + x = 1.368697678 Solving 0.2 + x = 1.368697678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 1.368697678 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.368697678 + -0.2 x = 1.368697678 + -0.2 Combine like terms: 1.368697678 + -0.2 = 1.168697678 x = 1.168697678 Simplifying x = 1.168697678Subproblem 2
x + 0.2 = -1.368697678 Simplifying x + 0.2 = -1.368697678 Reorder the terms: 0.2 + x = -1.368697678 Solving 0.2 + x = -1.368697678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -1.368697678 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.368697678 + -0.2 x = -1.368697678 + -0.2 Combine like terms: -1.368697678 + -0.2 = -1.568697678 x = -1.568697678 Simplifying x = -1.568697678Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.168697678, -1.568697678}
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