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Simplifying 9x2 + -7x + -11 = 24 Reorder the terms: -11 + -7x + 9x2 = 24 Solving -11 + -7x + 9x2 = 24 Solving for variable 'x'. Reorder the terms: -11 + -24 + -7x + 9x2 = 24 + -24 Combine like terms: -11 + -24 = -35 -35 + -7x + 9x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -35 + -7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.888888889 + -0.7777777778x + x2 = 0 Move the constant term to the right: Add '3.888888889' to each side of the equation. -3.888888889 + -0.7777777778x + 3.888888889 + x2 = 0 + 3.888888889 Reorder the terms: -3.888888889 + 3.888888889 + -0.7777777778x + x2 = 0 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + -0.7777777778x + x2 = 0 + 3.888888889 -0.7777777778x + x2 = 0 + 3.888888889 Combine like terms: 0 + 3.888888889 = 3.888888889 -0.7777777778x + x2 = 3.888888889 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 = 3.888888889 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778x + x2 = 3.888888889 + 0.1512345679 Combine like terms: 3.888888889 + 0.1512345679 = 4.0401234569 0.1512345679 + -0.7777777778x + x2 = 4.0401234569 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = 4.0401234569 Calculate the square root of the right side: 2.010005835 Break this problem into two subproblems by setting (x + -0.3888888889) equal to 2.010005835 and -2.010005835.Subproblem 1
x + -0.3888888889 = 2.010005835 Simplifying x + -0.3888888889 = 2.010005835 Reorder the terms: -0.3888888889 + x = 2.010005835 Solving -0.3888888889 + x = 2.010005835 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 = 2.010005835 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 2.010005835 + 0.3888888889 x = 2.010005835 + 0.3888888889 Combine like terms: 2.010005835 + 0.3888888889 = 2.3988947239 x = 2.3988947239 Simplifying x = 2.3988947239Subproblem 2
x + -0.3888888889 = -2.010005835 Simplifying x + -0.3888888889 = -2.010005835 Reorder the terms: -0.3888888889 + x = -2.010005835 Solving -0.3888888889 + x = -2.010005835 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 = -2.010005835 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -2.010005835 + 0.3888888889 x = -2.010005835 + 0.3888888889 Combine like terms: -2.010005835 + 0.3888888889 = -1.6211169461 x = -1.6211169461 Simplifying x = -1.6211169461Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3988947239, -1.6211169461}
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