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Simplifying x2 + -4x + 7 = 5x2 + -3x + -6 Reorder the terms: 7 + -4x + x2 = 5x2 + -3x + -6 Reorder the terms: 7 + -4x + x2 = -6 + -3x + 5x2 Solving 7 + -4x + x2 = -6 + -3x + 5x2 Solving for variable 'x'. Reorder the terms: 7 + 6 + -4x + 3x + x2 + -5x2 = -6 + -3x + 5x2 + 6 + 3x + -5x2 Combine like terms: 7 + 6 = 13 13 + -4x + 3x + x2 + -5x2 = -6 + -3x + 5x2 + 6 + 3x + -5x2 Combine like terms: -4x + 3x = -1x 13 + -1x + x2 + -5x2 = -6 + -3x + 5x2 + 6 + 3x + -5x2 Combine like terms: x2 + -5x2 = -4x2 13 + -1x + -4x2 = -6 + -3x + 5x2 + 6 + 3x + -5x2 Reorder the terms: 13 + -1x + -4x2 = -6 + 6 + -3x + 3x + 5x2 + -5x2 Combine like terms: -6 + 6 = 0 13 + -1x + -4x2 = 0 + -3x + 3x + 5x2 + -5x2 13 + -1x + -4x2 = -3x + 3x + 5x2 + -5x2 Combine like terms: -3x + 3x = 0 13 + -1x + -4x2 = 0 + 5x2 + -5x2 13 + -1x + -4x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 13 + -1x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3.25 + 0.25x + x2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + 0.25x + 3.25 + x2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + 0.25x + x2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + 0.25x + x2 = 0 + 3.25 0.25x + x2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 0.25x + x2 = 3.25 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 3.25 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 3.25 + 0.015625 Combine like terms: 3.25 + 0.015625 = 3.265625 0.015625 + 0.25x + x2 = 3.265625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (x + 0.125) equal to 1.807104037 and -1.807104037.Subproblem 1
x + 0.125 = 1.807104037 Simplifying x + 0.125 = 1.807104037 Reorder the terms: 0.125 + x = 1.807104037 Solving 0.125 + x = 1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 1.807104037 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.807104037 + -0.125 x = 1.807104037 + -0.125 Combine like terms: 1.807104037 + -0.125 = 1.682104037 x = 1.682104037 Simplifying x = 1.682104037Subproblem 2
x + 0.125 = -1.807104037 Simplifying x + 0.125 = -1.807104037 Reorder the terms: 0.125 + x = -1.807104037 Solving 0.125 + x = -1.807104037 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -1.807104037 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.807104037 + -0.125 x = -1.807104037 + -0.125 Combine like terms: -1.807104037 + -0.125 = -1.932104037 x = -1.932104037 Simplifying x = -1.932104037Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.682104037, -1.932104037}
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