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Simplifying 12x + -9(x + -1) * x = 2 Reorder the terms: 12x + -9(-1 + x) * x = 2 Reorder the terms for easier multiplication: 12x + -9x(-1 + x) = 2 12x + (-1 * -9x + x * -9x) = 2 12x + (9x + -9x2) = 2 Combine like terms: 12x + 9x = 21x 21x + -9x2 = 2 Solving 21x + -9x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 21x + -9x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 21x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 0.2222222222 + -2.333333333x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -2.333333333x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -2.333333333x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -2.333333333x + x2 = 0 + -0.2222222222 -2.333333333x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -2.333333333x + x2 = -0.2222222222 The x term is -2.333333333x. Take half its coefficient (-1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. -2.333333333x + 1.361111112 + x2 = -0.2222222222 + 1.361111112 Reorder the terms: 1.361111112 + -2.333333333x + x2 = -0.2222222222 + 1.361111112 Combine like terms: -0.2222222222 + 1.361111112 = 1.1388888898 1.361111112 + -2.333333333x + x2 = 1.1388888898 Factor a perfect square on the left side: (x + -1.166666667)(x + -1.166666667) = 1.1388888898 Calculate the square root of the right side: 1.067187373 Break this problem into two subproblems by setting (x + -1.166666667) equal to 1.067187373 and -1.067187373.Subproblem 1
x + -1.166666667 = 1.067187373 Simplifying x + -1.166666667 = 1.067187373 Reorder the terms: -1.166666667 + x = 1.067187373 Solving -1.166666667 + x = 1.067187373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = 1.067187373 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = 1.067187373 + 1.166666667 x = 1.067187373 + 1.166666667 Combine like terms: 1.067187373 + 1.166666667 = 2.23385404 x = 2.23385404 Simplifying x = 2.23385404Subproblem 2
x + -1.166666667 = -1.067187373 Simplifying x + -1.166666667 = -1.067187373 Reorder the terms: -1.166666667 + x = -1.067187373 Solving -1.166666667 + x = -1.067187373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.166666667' to each side of the equation. -1.166666667 + 1.166666667 + x = -1.067187373 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + x = -1.067187373 + 1.166666667 x = -1.067187373 + 1.166666667 Combine like terms: -1.067187373 + 1.166666667 = 0.099479294 x = 0.099479294 Simplifying x = 0.099479294Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.23385404, 0.099479294}
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