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Simplifying 9x2 + -6x + -6x + 4 = 22 Reorder the terms: 4 + -6x + -6x + 9x2 = 22 Combine like terms: -6x + -6x = -12x 4 + -12x + 9x2 = 22 Solving 4 + -12x + 9x2 = 22 Solving for variable 'x'. Reorder the terms: 4 + -22 + -12x + 9x2 = 22 + -22 Combine like terms: 4 + -22 = -18 -18 + -12x + 9x2 = 22 + -22 Combine like terms: 22 + -22 = 0 -18 + -12x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + -4x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + -4x + 3x2)' equal to zero and attempt to solve: Simplifying -6 + -4x + 3x2 = 0 Solving -6 + -4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -1.333333333x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -1.333333333x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1.333333333x + x2 = 0 + 2 -1.333333333x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -1.333333333x + x2 = 2 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 2 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 2 + 0.4444444442 Combine like terms: 2 + 0.4444444442 = 2.4444444442 0.4444444442 + -1.333333333x + x2 = 2.4444444442 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 2.4444444442 Calculate the square root of the right side: 1.56347192 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 1.56347192 and -1.56347192.Subproblem 1
x + -0.6666666665 = 1.56347192 Simplifying x + -0.6666666665 = 1.56347192 Reorder the terms: -0.6666666665 + x = 1.56347192 Solving -0.6666666665 + x = 1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 1.56347192 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.56347192 + 0.6666666665 x = 1.56347192 + 0.6666666665 Combine like terms: 1.56347192 + 0.6666666665 = 2.2301385865 x = 2.2301385865 Simplifying x = 2.2301385865Subproblem 2
x + -0.6666666665 = -1.56347192 Simplifying x + -0.6666666665 = -1.56347192 Reorder the terms: -0.6666666665 + x = -1.56347192 Solving -0.6666666665 + x = -1.56347192 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -1.56347192 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.56347192 + 0.6666666665 x = -1.56347192 + 0.6666666665 Combine like terms: -1.56347192 + 0.6666666665 = -0.8968052535 x = -0.8968052535 Simplifying x = -0.8968052535Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2301385865, -0.8968052535}Solution
x = {2.2301385865, -0.8968052535}
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