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Simplifying (3x2 + -5x + 7) + -1(12 + -5x2 + 3x) = 0 Reorder the terms: (7 + -5x + 3x2) + -1(12 + -5x2 + 3x) = 0 Remove parenthesis around (7 + -5x + 3x2) 7 + -5x + 3x2 + -1(12 + -5x2 + 3x) = 0 Reorder the terms: 7 + -5x + 3x2 + -1(12 + 3x + -5x2) = 0 7 + -5x + 3x2 + (12 * -1 + 3x * -1 + -5x2 * -1) = 0 7 + -5x + 3x2 + (-12 + -3x + 5x2) = 0 Reorder the terms: 7 + -12 + -5x + -3x + 3x2 + 5x2 = 0 Combine like terms: 7 + -12 = -5 -5 + -5x + -3x + 3x2 + 5x2 = 0 Combine like terms: -5x + -3x = -8x -5 + -8x + 3x2 + 5x2 = 0 Combine like terms: 3x2 + 5x2 = 8x2 -5 + -8x + 8x2 = 0 Solving -5 + -8x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -1x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -1x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -1x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -1x + x2 = 0 + 0.625 -1x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -1x + x2 = 0.625 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.625 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.625 + 0.25 Combine like terms: 0.625 + 0.25 = 0.875 0.25 + -1x + x2 = 0.875 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.875 Calculate the square root of the right side: 0.935414347 Break this problem into two subproblems by setting (x + -0.5) equal to 0.935414347 and -0.935414347.Subproblem 1
x + -0.5 = 0.935414347 Simplifying x + -0.5 = 0.935414347 Reorder the terms: -0.5 + x = 0.935414347 Solving -0.5 + x = 0.935414347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.935414347 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.935414347 + 0.5 x = 0.935414347 + 0.5 Combine like terms: 0.935414347 + 0.5 = 1.435414347 x = 1.435414347 Simplifying x = 1.435414347Subproblem 2
x + -0.5 = -0.935414347 Simplifying x + -0.5 = -0.935414347 Reorder the terms: -0.5 + x = -0.935414347 Solving -0.5 + x = -0.935414347 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.935414347 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.935414347 + 0.5 x = -0.935414347 + 0.5 Combine like terms: -0.935414347 + 0.5 = -0.435414347 x = -0.435414347 Simplifying x = -0.435414347Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.435414347, -0.435414347}
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