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Simplifying (-12x2 + 2x) + -1(5x2 + 6x + -4) = 0 Reorder the terms: (2x + -12x2) + -1(5x2 + 6x + -4) = 0 Remove parenthesis around (2x + -12x2) 2x + -12x2 + -1(5x2 + 6x + -4) = 0 Reorder the terms: 2x + -12x2 + -1(-4 + 6x + 5x2) = 0 2x + -12x2 + (-4 * -1 + 6x * -1 + 5x2 * -1) = 0 2x + -12x2 + (4 + -6x + -5x2) = 0 Reorder the terms: 4 + 2x + -6x + -12x2 + -5x2 = 0 Combine like terms: 2x + -6x = -4x 4 + -4x + -12x2 + -5x2 = 0 Combine like terms: -12x2 + -5x2 = -17x2 4 + -4x + -17x2 = 0 Solving 4 + -4x + -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'. -0.2352941176 + 0.2352941176x + x2 = 0 Move the constant term to the right: Add '0.2352941176' to each side of the equation. -0.2352941176 + 0.2352941176x + 0.2352941176 + x2 = 0 + 0.2352941176 Reorder the terms: -0.2352941176 + 0.2352941176 + 0.2352941176x + x2 = 0 + 0.2352941176 Combine like terms: -0.2352941176 + 0.2352941176 = 0.0000000000 0.0000000000 + 0.2352941176x + x2 = 0 + 0.2352941176 0.2352941176x + x2 = 0 + 0.2352941176 Combine like terms: 0 + 0.2352941176 = 0.2352941176 0.2352941176x + x2 = 0.2352941176 The x term is 0.2352941176x. Take half its coefficient (0.1176470588). Square it (0.01384083044) and add it to both sides. Add '0.01384083044' to each side of the equation. 0.2352941176x + 0.01384083044 + x2 = 0.2352941176 + 0.01384083044 Reorder the terms: 0.01384083044 + 0.2352941176x + x2 = 0.2352941176 + 0.01384083044 Combine like terms: 0.2352941176 + 0.01384083044 = 0.24913494804 0.01384083044 + 0.2352941176x + x2 = 0.24913494804 Factor a perfect square on the left side: (x + 0.1176470588)(x + 0.1176470588) = 0.24913494804 Calculate the square root of the right side: 0.499134198 Break this problem into two subproblems by setting (x + 0.1176470588) equal to 0.499134198 and -0.499134198.Subproblem 1
x + 0.1176470588 = 0.499134198 Simplifying x + 0.1176470588 = 0.499134198 Reorder the terms: 0.1176470588 + x = 0.499134198 Solving 0.1176470588 + x = 0.499134198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1176470588' to each side of the equation. 0.1176470588 + -0.1176470588 + x = 0.499134198 + -0.1176470588 Combine like terms: 0.1176470588 + -0.1176470588 = 0.0000000000 0.0000000000 + x = 0.499134198 + -0.1176470588 x = 0.499134198 + -0.1176470588 Combine like terms: 0.499134198 + -0.1176470588 = 0.3814871392 x = 0.3814871392 Simplifying x = 0.3814871392Subproblem 2
x + 0.1176470588 = -0.499134198 Simplifying x + 0.1176470588 = -0.499134198 Reorder the terms: 0.1176470588 + x = -0.499134198 Solving 0.1176470588 + x = -0.499134198 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1176470588' to each side of the equation. 0.1176470588 + -0.1176470588 + x = -0.499134198 + -0.1176470588 Combine like terms: 0.1176470588 + -0.1176470588 = 0.0000000000 0.0000000000 + x = -0.499134198 + -0.1176470588 x = -0.499134198 + -0.1176470588 Combine like terms: -0.499134198 + -0.1176470588 = -0.6167812568 x = -0.6167812568 Simplifying x = -0.6167812568Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3814871392, -0.6167812568}
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