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Simplifying 0 = 12x2 + 12x + -23 Reorder the terms: 0 = -23 + 12x + 12x2 Solving 0 = -23 + 12x + 12x2 Solving for variable 'x'. Combine like terms: 0 + 23 = 23 23 + -12x + -12x2 = -23 + 12x + 12x2 + 23 + -12x + -12x2 Reorder the terms: 23 + -12x + -12x2 = -23 + 23 + 12x + -12x + 12x2 + -12x2 Combine like terms: -23 + 23 = 0 23 + -12x + -12x2 = 0 + 12x + -12x + 12x2 + -12x2 23 + -12x + -12x2 = 12x + -12x + 12x2 + -12x2 Combine like terms: 12x + -12x = 0 23 + -12x + -12x2 = 0 + 12x2 + -12x2 23 + -12x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 23 + -12x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -1.916666667 + x + x2 = 0 Move the constant term to the right: Add '1.916666667' to each side of the equation. -1.916666667 + x + 1.916666667 + x2 = 0 + 1.916666667 Reorder the terms: -1.916666667 + 1.916666667 + x + x2 = 0 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x + x2 = 0 + 1.916666667 x + x2 = 0 + 1.916666667 Combine like terms: 0 + 1.916666667 = 1.916666667 x + x2 = 1.916666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 1.916666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.916666667 + 0.25 Combine like terms: 1.916666667 + 0.25 = 2.166666667 1.25 + x2 = 2.166666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.166666667 Calculate the square root of the right side: 1.471960145 Break this problem into two subproblems by setting (x + 0.5) equal to 1.471960145 and -1.471960145.Subproblem 1
x + 0.5 = 1.471960145 Simplifying x + 0.5 = 1.471960145 Reorder the terms: 0.5 + x = 1.471960145 Solving 0.5 + x = 1.471960145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.471960145 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.471960145 + -0.5 x = 1.471960145 + -0.5 Combine like terms: 1.471960145 + -0.5 = 0.971960145 x = 0.971960145 Simplifying x = 0.971960145Subproblem 2
x + 0.5 = -1.471960145 Simplifying x + 0.5 = -1.471960145 Reorder the terms: 0.5 + x = -1.471960145 Solving 0.5 + x = -1.471960145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.471960145 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.471960145 + -0.5 x = -1.471960145 + -0.5 Combine like terms: -1.471960145 + -0.5 = -1.971960145 x = -1.971960145 Simplifying x = -1.971960145Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.971960145, -1.971960145}
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