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Simplifying (-12x2 + 4x) + -1(5x2 + 7x + -3) = 0 Reorder the terms: (4x + -12x2) + -1(5x2 + 7x + -3) = 0 Remove parenthesis around (4x + -12x2) 4x + -12x2 + -1(5x2 + 7x + -3) = 0 Reorder the terms: 4x + -12x2 + -1(-3 + 7x + 5x2) = 0 4x + -12x2 + (-3 * -1 + 7x * -1 + 5x2 * -1) = 0 4x + -12x2 + (3 + -7x + -5x2) = 0 Reorder the terms: 3 + 4x + -7x + -12x2 + -5x2 = 0 Combine like terms: 4x + -7x = -3x 3 + -3x + -12x2 + -5x2 = 0 Combine like terms: -12x2 + -5x2 = -17x2 3 + -3x + -17x2 = 0 Solving 3 + -3x + -17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. -0.1764705882 + 0.1764705882x + x2 = 0 Move the constant term to the right: Add '0.1764705882' to each side of the equation. -0.1764705882 + 0.1764705882x + 0.1764705882 + x2 = 0 + 0.1764705882 Reorder the terms: -0.1764705882 + 0.1764705882 + 0.1764705882x + x2 = 0 + 0.1764705882 Combine like terms: -0.1764705882 + 0.1764705882 = 0.0000000000 0.0000000000 + 0.1764705882x + x2 = 0 + 0.1764705882 0.1764705882x + x2 = 0 + 0.1764705882 Combine like terms: 0 + 0.1764705882 = 0.1764705882 0.1764705882x + x2 = 0.1764705882 The x term is 0.1764705882x. Take half its coefficient (0.0882352941). Square it (0.007785467125) and add it to both sides. Add '0.007785467125' to each side of the equation. 0.1764705882x + 0.007785467125 + x2 = 0.1764705882 + 0.007785467125 Reorder the terms: 0.007785467125 + 0.1764705882x + x2 = 0.1764705882 + 0.007785467125 Combine like terms: 0.1764705882 + 0.007785467125 = 0.184256055325 0.007785467125 + 0.1764705882x + x2 = 0.184256055325 Factor a perfect square on the left side: (x + 0.0882352941)(x + 0.0882352941) = 0.184256055325 Calculate the square root of the right side: 0.429250574 Break this problem into two subproblems by setting (x + 0.0882352941) equal to 0.429250574 and -0.429250574.Subproblem 1
x + 0.0882352941 = 0.429250574 Simplifying x + 0.0882352941 = 0.429250574 Reorder the terms: 0.0882352941 + x = 0.429250574 Solving 0.0882352941 + x = 0.429250574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0882352941' to each side of the equation. 0.0882352941 + -0.0882352941 + x = 0.429250574 + -0.0882352941 Combine like terms: 0.0882352941 + -0.0882352941 = 0.0000000000 0.0000000000 + x = 0.429250574 + -0.0882352941 x = 0.429250574 + -0.0882352941 Combine like terms: 0.429250574 + -0.0882352941 = 0.3410152799 x = 0.3410152799 Simplifying x = 0.3410152799Subproblem 2
x + 0.0882352941 = -0.429250574 Simplifying x + 0.0882352941 = -0.429250574 Reorder the terms: 0.0882352941 + x = -0.429250574 Solving 0.0882352941 + x = -0.429250574 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0882352941' to each side of the equation. 0.0882352941 + -0.0882352941 + x = -0.429250574 + -0.0882352941 Combine like terms: 0.0882352941 + -0.0882352941 = 0.0000000000 0.0000000000 + x = -0.429250574 + -0.0882352941 x = -0.429250574 + -0.0882352941 Combine like terms: -0.429250574 + -0.0882352941 = -0.5174858681 x = -0.5174858681 Simplifying x = -0.5174858681Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3410152799, -0.5174858681}
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