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Simplifying -3x2 + -7 + 2x + 17x2 + -12x = 0 Reorder the terms: -7 + 2x + -12x + -3x2 + 17x2 = 0 Combine like terms: 2x + -12x = -10x -7 + -10x + -3x2 + 17x2 = 0 Combine like terms: -3x2 + 17x2 = 14x2 -7 + -10x + 14x2 = 0 Solving -7 + -10x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.5 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.7142857143x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.7142857143x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.7142857143x + x2 = 0 + 0.5 -0.7142857143x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.7142857143x + x2 = 0.5 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 0.5 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 0.5 + 0.1275510204 Combine like terms: 0.5 + 0.1275510204 = 0.6275510204 0.1275510204 + -0.7142857143x + x2 = 0.6275510204 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 0.6275510204 Calculate the square root of the right side: 0.792181179 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 0.792181179 and -0.792181179.Subproblem 1
x + -0.3571428572 = 0.792181179 Simplifying x + -0.3571428572 = 0.792181179 Reorder the terms: -0.3571428572 + x = 0.792181179 Solving -0.3571428572 + x = 0.792181179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 0.792181179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 0.792181179 + 0.3571428572 x = 0.792181179 + 0.3571428572 Combine like terms: 0.792181179 + 0.3571428572 = 1.1493240362 x = 1.1493240362 Simplifying x = 1.1493240362Subproblem 2
x + -0.3571428572 = -0.792181179 Simplifying x + -0.3571428572 = -0.792181179 Reorder the terms: -0.3571428572 + x = -0.792181179 Solving -0.3571428572 + x = -0.792181179 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -0.792181179 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -0.792181179 + 0.3571428572 x = -0.792181179 + 0.3571428572 Combine like terms: -0.792181179 + 0.3571428572 = -0.4350383218 x = -0.4350383218 Simplifying x = -0.4350383218Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1493240362, -0.4350383218}
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