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Simplifying 12x + -3x + 11 = 4x(17 + -9x) Reorder the terms: 11 + 12x + -3x = 4x(17 + -9x) Combine like terms: 12x + -3x = 9x 11 + 9x = 4x(17 + -9x) 11 + 9x = (17 * 4x + -9x * 4x) 11 + 9x = (68x + -36x2) Solving 11 + 9x = 68x + -36x2 Solving for variable 'x'. Combine like terms: 9x + -68x = -59x 11 + -59x + 36x2 = 68x + -36x2 + -68x + 36x2 Reorder the terms: 11 + -59x + 36x2 = 68x + -68x + -36x2 + 36x2 Combine like terms: 68x + -68x = 0 11 + -59x + 36x2 = 0 + -36x2 + 36x2 11 + -59x + 36x2 = -36x2 + 36x2 Combine like terms: -36x2 + 36x2 = 0 11 + -59x + 36x2 = 0 Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.3055555556 + -1.638888889x + x2 = 0 Move the constant term to the right: Add '-0.3055555556' to each side of the equation. 0.3055555556 + -1.638888889x + -0.3055555556 + x2 = 0 + -0.3055555556 Reorder the terms: 0.3055555556 + -0.3055555556 + -1.638888889x + x2 = 0 + -0.3055555556 Combine like terms: 0.3055555556 + -0.3055555556 = 0.0000000000 0.0000000000 + -1.638888889x + x2 = 0 + -0.3055555556 -1.638888889x + x2 = 0 + -0.3055555556 Combine like terms: 0 + -0.3055555556 = -0.3055555556 -1.638888889x + x2 = -0.3055555556 The x term is -1.638888889x. Take half its coefficient (-0.8194444445). Square it (0.6714891976) and add it to both sides. Add '0.6714891976' to each side of the equation. -1.638888889x + 0.6714891976 + x2 = -0.3055555556 + 0.6714891976 Reorder the terms: 0.6714891976 + -1.638888889x + x2 = -0.3055555556 + 0.6714891976 Combine like terms: -0.3055555556 + 0.6714891976 = 0.365933642 0.6714891976 + -1.638888889x + x2 = 0.365933642 Factor a perfect square on the left side: (x + -0.8194444445)(x + -0.8194444445) = 0.365933642 Calculate the square root of the right side: 0.604924493 Break this problem into two subproblems by setting (x + -0.8194444445) equal to 0.604924493 and -0.604924493.Subproblem 1
x + -0.8194444445 = 0.604924493 Simplifying x + -0.8194444445 = 0.604924493 Reorder the terms: -0.8194444445 + x = 0.604924493 Solving -0.8194444445 + x = 0.604924493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8194444445' to each side of the equation. -0.8194444445 + 0.8194444445 + x = 0.604924493 + 0.8194444445 Combine like terms: -0.8194444445 + 0.8194444445 = 0.0000000000 0.0000000000 + x = 0.604924493 + 0.8194444445 x = 0.604924493 + 0.8194444445 Combine like terms: 0.604924493 + 0.8194444445 = 1.4243689375 x = 1.4243689375 Simplifying x = 1.4243689375Subproblem 2
x + -0.8194444445 = -0.604924493 Simplifying x + -0.8194444445 = -0.604924493 Reorder the terms: -0.8194444445 + x = -0.604924493 Solving -0.8194444445 + x = -0.604924493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8194444445' to each side of the equation. -0.8194444445 + 0.8194444445 + x = -0.604924493 + 0.8194444445 Combine like terms: -0.8194444445 + 0.8194444445 = 0.0000000000 0.0000000000 + x = -0.604924493 + 0.8194444445 x = -0.604924493 + 0.8194444445 Combine like terms: -0.604924493 + 0.8194444445 = 0.2145199515 x = 0.2145199515 Simplifying x = 0.2145199515Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4243689375, 0.2145199515}
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