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Simplifying 40x + 18x(x + -3) = 468 Reorder the terms: 40x + 18x(-3 + x) = 468 40x + (-3 * 18x + x * 18x) = 468 40x + (-54x + 18x2) = 468 Combine like terms: 40x + -54x = -14x -14x + 18x2 = 468 Solving -14x + 18x2 = 468 Solving for variable 'x'. Reorder the terms: -468 + -14x + 18x2 = 468 + -468 Combine like terms: 468 + -468 = 0 -468 + -14x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-234 + -7x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-234 + -7x + 9x2)' equal to zero and attempt to solve: Simplifying -234 + -7x + 9x2 = 0 Solving -234 + -7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -26 + -0.7777777778x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + -0.7777777778x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -0.7777777778x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -0.7777777778x + x2 = 0 + 26 -0.7777777778x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -0.7777777778x + x2 = 26 The x term is -0.7777777778x. Take half its coefficient (-0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. -0.7777777778x + 0.1512345679 + x2 = 26 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778x + x2 = 26 + 0.1512345679 Combine like terms: 26 + 0.1512345679 = 26.1512345679 0.1512345679 + -0.7777777778x + x2 = 26.1512345679 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = 26.1512345679 Calculate the square root of the right side: 5.11382778 Break this problem into two subproblems by setting (x + -0.3888888889) equal to 5.11382778 and -5.11382778.Subproblem 1
x + -0.3888888889 = 5.11382778 Simplifying x + -0.3888888889 = 5.11382778 Reorder the terms: -0.3888888889 + x = 5.11382778 Solving -0.3888888889 + x = 5.11382778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = 5.11382778 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 5.11382778 + 0.3888888889 x = 5.11382778 + 0.3888888889 Combine like terms: 5.11382778 + 0.3888888889 = 5.5027166689 x = 5.5027166689 Simplifying x = 5.5027166689Subproblem 2
x + -0.3888888889 = -5.11382778 Simplifying x + -0.3888888889 = -5.11382778 Reorder the terms: -0.3888888889 + x = -5.11382778 Solving -0.3888888889 + x = -5.11382778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + x = -5.11382778 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -5.11382778 + 0.3888888889 x = -5.11382778 + 0.3888888889 Combine like terms: -5.11382778 + 0.3888888889 = -4.7249388911 x = -4.7249388911 Simplifying x = -4.7249388911Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.5027166689, -4.7249388911}Solution
x = {5.5027166689, -4.7249388911}
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