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Simplifying (3x)(3x) + -1x + -12 = 0 Remove parenthesis around (3x) 3x(3x) + -1x + -12 = 0 Remove parenthesis around (3x) 3x * 3x + -1x + -12 = 0 Reorder the terms for easier multiplication: 3 * 3x * x + -1x + -12 = 0 Multiply 3 * 3 9x * x + -1x + -12 = 0 Multiply x * x 9x2 + -1x + -12 = 0 Reorder the terms: -12 + -1x + 9x2 = 0 Solving -12 + -1x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.333333333 + -0.1111111111x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -0.1111111111x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -0.1111111111x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -0.1111111111x + x2 = 0 + 1.333333333 -0.1111111111x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -0.1111111111x + x2 = 1.333333333 The x term is -0.1111111111x. Take half its coefficient (-0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. -0.1111111111x + 0.003086419752 + x2 = 1.333333333 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111x + x2 = 1.333333333 + 0.003086419752 Combine like terms: 1.333333333 + 0.003086419752 = 1.336419752752 0.003086419752 + -0.1111111111x + x2 = 1.336419752752 Factor a perfect square on the left side: (x + -0.05555555555)(x + -0.05555555555) = 1.336419752752 Calculate the square root of the right side: 1.156036225 Break this problem into two subproblems by setting (x + -0.05555555555) equal to 1.156036225 and -1.156036225.Subproblem 1
x + -0.05555555555 = 1.156036225 Simplifying x + -0.05555555555 = 1.156036225 Reorder the terms: -0.05555555555 + x = 1.156036225 Solving -0.05555555555 + x = 1.156036225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = 1.156036225 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = 1.156036225 + 0.05555555555 x = 1.156036225 + 0.05555555555 Combine like terms: 1.156036225 + 0.05555555555 = 1.21159178055 x = 1.21159178055 Simplifying x = 1.21159178055Subproblem 2
x + -0.05555555555 = -1.156036225 Simplifying x + -0.05555555555 = -1.156036225 Reorder the terms: -0.05555555555 + x = -1.156036225 Solving -0.05555555555 + x = -1.156036225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.05555555555' to each side of the equation. -0.05555555555 + 0.05555555555 + x = -1.156036225 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + x = -1.156036225 + 0.05555555555 x = -1.156036225 + 0.05555555555 Combine like terms: -1.156036225 + 0.05555555555 = -1.10048066945 x = -1.10048066945 Simplifying x = -1.10048066945Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.21159178055, -1.10048066945}
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