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Simplifying -12x2 + 18x + 12 = 5 Reorder the terms: 12 + 18x + -12x2 = 5 Solving 12 + 18x + -12x2 = 5 Solving for variable 'x'. Reorder the terms: 12 + -5 + 18x + -12x2 = 5 + -5 Combine like terms: 12 + -5 = 7 7 + 18x + -12x2 = 5 + -5 Combine like terms: 5 + -5 = 0 7 + 18x + -12x2 = 0 Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -0.5833333333 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.5833333333' to each side of the equation. -0.5833333333 + -1.5x + 0.5833333333 + x2 = 0 + 0.5833333333 Reorder the terms: -0.5833333333 + 0.5833333333 + -1.5x + x2 = 0 + 0.5833333333 Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000 0.0000000000 + -1.5x + x2 = 0 + 0.5833333333 -1.5x + x2 = 0 + 0.5833333333 Combine like terms: 0 + 0.5833333333 = 0.5833333333 -1.5x + x2 = 0.5833333333 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.5833333333 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.5833333333 + 0.5625 Combine like terms: 0.5833333333 + 0.5625 = 1.1458333333 0.5625 + -1.5x + x2 = 1.1458333333 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.1458333333 Calculate the square root of the right side: 1.070436048 Break this problem into two subproblems by setting (x + -0.75) equal to 1.070436048 and -1.070436048.Subproblem 1
x + -0.75 = 1.070436048 Simplifying x + -0.75 = 1.070436048 Reorder the terms: -0.75 + x = 1.070436048 Solving -0.75 + x = 1.070436048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.070436048 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.070436048 + 0.75 x = 1.070436048 + 0.75 Combine like terms: 1.070436048 + 0.75 = 1.820436048 x = 1.820436048 Simplifying x = 1.820436048Subproblem 2
x + -0.75 = -1.070436048 Simplifying x + -0.75 = -1.070436048 Reorder the terms: -0.75 + x = -1.070436048 Solving -0.75 + x = -1.070436048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.070436048 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.070436048 + 0.75 x = -1.070436048 + 0.75 Combine like terms: -1.070436048 + 0.75 = -0.320436048 x = -0.320436048 Simplifying x = -0.320436048Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.820436048, -0.320436048}
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