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Simplifying 9x(12x + -11) = 225 Reorder the terms: 9x(-11 + 12x) = 225 (-11 * 9x + 12x * 9x) = 225 (-99x + 108x2) = 225 Solving -99x + 108x2 = 225 Solving for variable 'x'. Reorder the terms: -225 + -99x + 108x2 = 225 + -225 Combine like terms: 225 + -225 = 0 -225 + -99x + 108x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-25 + -11x + 12x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-25 + -11x + 12x2)' equal to zero and attempt to solve: Simplifying -25 + -11x + 12x2 = 0 Solving -25 + -11x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -2.083333333 + -0.9166666667x + x2 = 0 Move the constant term to the right: Add '2.083333333' to each side of the equation. -2.083333333 + -0.9166666667x + 2.083333333 + x2 = 0 + 2.083333333 Reorder the terms: -2.083333333 + 2.083333333 + -0.9166666667x + x2 = 0 + 2.083333333 Combine like terms: -2.083333333 + 2.083333333 = 0.000000000 0.000000000 + -0.9166666667x + x2 = 0 + 2.083333333 -0.9166666667x + x2 = 0 + 2.083333333 Combine like terms: 0 + 2.083333333 = 2.083333333 -0.9166666667x + x2 = 2.083333333 The x term is -0.9166666667x. Take half its coefficient (-0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. -0.9166666667x + 0.2100694445 + x2 = 2.083333333 + 0.2100694445 Reorder the terms: 0.2100694445 + -0.9166666667x + x2 = 2.083333333 + 0.2100694445 Combine like terms: 2.083333333 + 0.2100694445 = 2.2934027775 0.2100694445 + -0.9166666667x + x2 = 2.2934027775 Factor a perfect square on the left side: (x + -0.4583333334)(x + -0.4583333334) = 2.2934027775 Calculate the square root of the right side: 1.514398487 Break this problem into two subproblems by setting (x + -0.4583333334) equal to 1.514398487 and -1.514398487.Subproblem 1
x + -0.4583333334 = 1.514398487 Simplifying x + -0.4583333334 = 1.514398487 Reorder the terms: -0.4583333334 + x = 1.514398487 Solving -0.4583333334 + x = 1.514398487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + x = 1.514398487 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = 1.514398487 + 0.4583333334 x = 1.514398487 + 0.4583333334 Combine like terms: 1.514398487 + 0.4583333334 = 1.9727318204 x = 1.9727318204 Simplifying x = 1.9727318204Subproblem 2
x + -0.4583333334 = -1.514398487 Simplifying x + -0.4583333334 = -1.514398487 Reorder the terms: -0.4583333334 + x = -1.514398487 Solving -0.4583333334 + x = -1.514398487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4583333334' to each side of the equation. -0.4583333334 + 0.4583333334 + x = -1.514398487 + 0.4583333334 Combine like terms: -0.4583333334 + 0.4583333334 = 0.0000000000 0.0000000000 + x = -1.514398487 + 0.4583333334 x = -1.514398487 + 0.4583333334 Combine like terms: -1.514398487 + 0.4583333334 = -1.0560651536 x = -1.0560651536 Simplifying x = -1.0560651536Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9727318204, -1.0560651536}Solution
x = {1.9727318204, -1.0560651536}
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