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Simplifying (-10x2 + -17x + 11) + -1(12x2 + -6x + -16) = 0 Reorder the terms: (11 + -17x + -10x2) + -1(12x2 + -6x + -16) = 0 Remove parenthesis around (11 + -17x + -10x2) 11 + -17x + -10x2 + -1(12x2 + -6x + -16) = 0 Reorder the terms: 11 + -17x + -10x2 + -1(-16 + -6x + 12x2) = 0 11 + -17x + -10x2 + (-16 * -1 + -6x * -1 + 12x2 * -1) = 0 11 + -17x + -10x2 + (16 + 6x + -12x2) = 0 Reorder the terms: 11 + 16 + -17x + 6x + -10x2 + -12x2 = 0 Combine like terms: 11 + 16 = 27 27 + -17x + 6x + -10x2 + -12x2 = 0 Combine like terms: -17x + 6x = -11x 27 + -11x + -10x2 + -12x2 = 0 Combine like terms: -10x2 + -12x2 = -22x2 27 + -11x + -22x2 = 0 Solving 27 + -11x + -22x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -22 the coefficient of the squared term: Divide each side by '-22'. -1.227272727 + 0.5x + x2 = 0 Move the constant term to the right: Add '1.227272727' to each side of the equation. -1.227272727 + 0.5x + 1.227272727 + x2 = 0 + 1.227272727 Reorder the terms: -1.227272727 + 1.227272727 + 0.5x + x2 = 0 + 1.227272727 Combine like terms: -1.227272727 + 1.227272727 = 0.000000000 0.000000000 + 0.5x + x2 = 0 + 1.227272727 0.5x + x2 = 0 + 1.227272727 Combine like terms: 0 + 1.227272727 = 1.227272727 0.5x + x2 = 1.227272727 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 1.227272727 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 1.227272727 + 0.0625 Combine like terms: 1.227272727 + 0.0625 = 1.289772727 0.0625 + 0.5x + x2 = 1.289772727 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 1.289772727 Calculate the square root of the right side: 1.135681613 Break this problem into two subproblems by setting (x + 0.25) equal to 1.135681613 and -1.135681613.Subproblem 1
x + 0.25 = 1.135681613 Simplifying x + 0.25 = 1.135681613 Reorder the terms: 0.25 + x = 1.135681613 Solving 0.25 + x = 1.135681613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.135681613 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.135681613 + -0.25 x = 1.135681613 + -0.25 Combine like terms: 1.135681613 + -0.25 = 0.885681613 x = 0.885681613 Simplifying x = 0.885681613Subproblem 2
x + 0.25 = -1.135681613 Simplifying x + 0.25 = -1.135681613 Reorder the terms: 0.25 + x = -1.135681613 Solving 0.25 + x = -1.135681613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.135681613 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.135681613 + -0.25 x = -1.135681613 + -0.25 Combine like terms: -1.135681613 + -0.25 = -1.385681613 x = -1.385681613 Simplifying x = -1.385681613Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.885681613, -1.385681613}
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