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Simplifying (11x + 6) * x = 12 Reorder the terms: (6 + 11x) * x = 12 Reorder the terms for easier multiplication: x(6 + 11x) = 12 (6 * x + 11x * x) = 12 (6x + 11x2) = 12 Solving 6x + 11x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 6x + 11x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 6x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -1.090909091 + 0.5454545455x + x2 = 0 Move the constant term to the right: Add '1.090909091' to each side of the equation. -1.090909091 + 0.5454545455x + 1.090909091 + x2 = 0 + 1.090909091 Reorder the terms: -1.090909091 + 1.090909091 + 0.5454545455x + x2 = 0 + 1.090909091 Combine like terms: -1.090909091 + 1.090909091 = 0.000000000 0.000000000 + 0.5454545455x + x2 = 0 + 1.090909091 0.5454545455x + x2 = 0 + 1.090909091 Combine like terms: 0 + 1.090909091 = 1.090909091 0.5454545455x + x2 = 1.090909091 The x term is 0.5454545455x. Take half its coefficient (0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. 0.5454545455x + 0.07438016533 + x2 = 1.090909091 + 0.07438016533 Reorder the terms: 0.07438016533 + 0.5454545455x + x2 = 1.090909091 + 0.07438016533 Combine like terms: 1.090909091 + 0.07438016533 = 1.16528925633 0.07438016533 + 0.5454545455x + x2 = 1.16528925633 Factor a perfect square on the left side: (x + 0.2727272728)(x + 0.2727272728) = 1.16528925633 Calculate the square root of the right side: 1.079485644 Break this problem into two subproblems by setting (x + 0.2727272728) equal to 1.079485644 and -1.079485644.Subproblem 1
x + 0.2727272728 = 1.079485644 Simplifying x + 0.2727272728 = 1.079485644 Reorder the terms: 0.2727272728 + x = 1.079485644 Solving 0.2727272728 + x = 1.079485644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + x = 1.079485644 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + x = 1.079485644 + -0.2727272728 x = 1.079485644 + -0.2727272728 Combine like terms: 1.079485644 + -0.2727272728 = 0.8067583712 x = 0.8067583712 Simplifying x = 0.8067583712Subproblem 2
x + 0.2727272728 = -1.079485644 Simplifying x + 0.2727272728 = -1.079485644 Reorder the terms: 0.2727272728 + x = -1.079485644 Solving 0.2727272728 + x = -1.079485644 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + x = -1.079485644 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + x = -1.079485644 + -0.2727272728 x = -1.079485644 + -0.2727272728 Combine like terms: -1.079485644 + -0.2727272728 = -1.3522129168 x = -1.3522129168 Simplifying x = -1.3522129168Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8067583712, -1.3522129168}
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