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Simplifying 5x2 + 4x = 2x2 + 12 Reorder the terms: 4x + 5x2 = 2x2 + 12 Reorder the terms: 4x + 5x2 = 12 + 2x2 Solving 4x + 5x2 = 12 + 2x2 Solving for variable 'x'. Reorder the terms: -12 + 4x + 5x2 + -2x2 = 12 + 2x2 + -12 + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -12 + 4x + 3x2 = 12 + 2x2 + -12 + -2x2 Reorder the terms: -12 + 4x + 3x2 = 12 + -12 + 2x2 + -2x2 Combine like terms: 12 + -12 = 0 -12 + 4x + 3x2 = 0 + 2x2 + -2x2 -12 + 4x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -12 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -4 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 1.333333333x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 1.333333333x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 1.333333333x + x2 = 0 + 4 1.333333333x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 1.333333333x + x2 = 4 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 = 4 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 4 + 0.4444444442 Combine like terms: 4 + 0.4444444442 = 4.4444444442 0.4444444442 + 1.333333333x + x2 = 4.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 4.4444444442 Calculate the square root of the right side: 2.108185107 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 2.108185107 and -2.108185107.Subproblem 1
x + 0.6666666665 = 2.108185107 Simplifying x + 0.6666666665 = 2.108185107 Reorder the terms: 0.6666666665 + x = 2.108185107 Solving 0.6666666665 + x = 2.108185107 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 = 2.108185107 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 2.108185107 + -0.6666666665 x = 2.108185107 + -0.6666666665 Combine like terms: 2.108185107 + -0.6666666665 = 1.4415184405 x = 1.4415184405 Simplifying x = 1.4415184405Subproblem 2
x + 0.6666666665 = -2.108185107 Simplifying x + 0.6666666665 = -2.108185107 Reorder the terms: 0.6666666665 + x = -2.108185107 Solving 0.6666666665 + x = -2.108185107 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 = -2.108185107 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -2.108185107 + -0.6666666665 x = -2.108185107 + -0.6666666665 Combine like terms: -2.108185107 + -0.6666666665 = -2.7748517735 x = -2.7748517735 Simplifying x = -2.7748517735Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4415184405, -2.7748517735}
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