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Simplifying (6x2 + -4x + 7) + (2x2 + -3x + -9) = 0 Reorder the terms: (7 + -4x + 6x2) + (2x2 + -3x + -9) = 0 Remove parenthesis around (7 + -4x + 6x2) 7 + -4x + 6x2 + (2x2 + -3x + -9) = 0 Reorder the terms: 7 + -4x + 6x2 + (-9 + -3x + 2x2) = 0 Remove parenthesis around (-9 + -3x + 2x2) 7 + -4x + 6x2 + -9 + -3x + 2x2 = 0 Reorder the terms: 7 + -9 + -4x + -3x + 6x2 + 2x2 = 0 Combine like terms: 7 + -9 = -2 -2 + -4x + -3x + 6x2 + 2x2 = 0 Combine like terms: -4x + -3x = -7x -2 + -7x + 6x2 + 2x2 = 0 Combine like terms: 6x2 + 2x2 = 8x2 -2 + -7x + 8x2 = 0 Solving -2 + -7x + 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'. -0.25 + -0.875x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -0.875x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -0.875x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -0.875x + x2 = 0 + 0.25 -0.875x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -0.875x + x2 = 0.25 The x term is -0.875x. Take half its coefficient (-0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. -0.875x + 0.19140625 + x2 = 0.25 + 0.19140625 Reorder the terms: 0.19140625 + -0.875x + x2 = 0.25 + 0.19140625 Combine like terms: 0.25 + 0.19140625 = 0.44140625 0.19140625 + -0.875x + x2 = 0.44140625 Factor a perfect square on the left side: (x + -0.4375)(x + -0.4375) = 0.44140625 Calculate the square root of the right side: 0.664384113 Break this problem into two subproblems by setting (x + -0.4375) equal to 0.664384113 and -0.664384113.Subproblem 1
x + -0.4375 = 0.664384113 Simplifying x + -0.4375 = 0.664384113 Reorder the terms: -0.4375 + x = 0.664384113 Solving -0.4375 + x = 0.664384113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = 0.664384113 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = 0.664384113 + 0.4375 x = 0.664384113 + 0.4375 Combine like terms: 0.664384113 + 0.4375 = 1.101884113 x = 1.101884113 Simplifying x = 1.101884113Subproblem 2
x + -0.4375 = -0.664384113 Simplifying x + -0.4375 = -0.664384113 Reorder the terms: -0.4375 + x = -0.664384113 Solving -0.4375 + x = -0.664384113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4375' to each side of the equation. -0.4375 + 0.4375 + x = -0.664384113 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + x = -0.664384113 + 0.4375 x = -0.664384113 + 0.4375 Combine like terms: -0.664384113 + 0.4375 = -0.226884113 x = -0.226884113 Simplifying x = -0.226884113Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.101884113, -0.226884113}
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