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Simplifying 9x2 + -7x + -11 = 12 Reorder the terms: -11 + -7x + 9x2 = 12 Solving -11 + -7x + 9x2 = 12 Solving for variable 'x'. Reorder the terms: -11 + -12 + -7x + 9x2 = 12 + -12 Combine like terms: -11 + -12 = -23 -23 + -7x + 9x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -23 + -7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.555555556 + -0.7777777778x + x2 = 0 Move the constant term to the right: Add '2.555555556' to each side of the equation. -2.555555556 + -0.7777777778x + 2.555555556 + x2 = 0 + 2.555555556 Reorder the terms: -2.555555556 + 2.555555556 + -0.7777777778x + x2 = 0 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + -0.7777777778x + x2 = 0 + 2.555555556 -0.7777777778x + x2 = 0 + 2.555555556 Combine like terms: 0 + 2.555555556 = 2.555555556 -0.7777777778x + x2 = 2.555555556 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 = 2.555555556 + 0.1512345679 Reorder the terms: 0.1512345679 + -0.7777777778x + x2 = 2.555555556 + 0.1512345679 Combine like terms: 2.555555556 + 0.1512345679 = 2.7067901239 0.1512345679 + -0.7777777778x + x2 = 2.7067901239 Factor a perfect square on the left side: (x + -0.3888888889)(x + -0.3888888889) = 2.7067901239 Calculate the square root of the right side: 1.645232544 Break this problem into two subproblems by setting (x + -0.3888888889) equal to 1.645232544 and -1.645232544.Subproblem 1
x + -0.3888888889 = 1.645232544 Simplifying x + -0.3888888889 = 1.645232544 Reorder the terms: -0.3888888889 + x = 1.645232544 Solving -0.3888888889 + x = 1.645232544 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 = 1.645232544 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = 1.645232544 + 0.3888888889 x = 1.645232544 + 0.3888888889 Combine like terms: 1.645232544 + 0.3888888889 = 2.0341214329 x = 2.0341214329 Simplifying x = 2.0341214329Subproblem 2
x + -0.3888888889 = -1.645232544 Simplifying x + -0.3888888889 = -1.645232544 Reorder the terms: -0.3888888889 + x = -1.645232544 Solving -0.3888888889 + x = -1.645232544 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 = -1.645232544 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + x = -1.645232544 + 0.3888888889 x = -1.645232544 + 0.3888888889 Combine like terms: -1.645232544 + 0.3888888889 = -1.2563436551 x = -1.2563436551 Simplifying x = -1.2563436551Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0341214329, -1.2563436551}
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