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Simplifying (4x2) + -1x + 5 = x + 9 Reorder the terms: 5 + -1x + (4x2) = x + 9 Reorder the terms: 5 + -1x + (4x2) = 9 + x Solving 5 + -1x + (4x2) = 9 + x Solving for variable 'x'. Reorder the terms: 5 + -9 + -1x + -1x + (4x2) = 9 + x + -9 + -1x Combine like terms: 5 + -9 = -4 -4 + -1x + -1x + (4x2) = 9 + x + -9 + -1x Combine like terms: -1x + -1x = -2x -4 + -2x + (4x2) = 9 + x + -9 + -1x Reorder the terms: -4 + -2x + (4x2) = 9 + -9 + x + -1x Combine like terms: 9 + -9 = 0 -4 + -2x + (4x2) = 0 + x + -1x -4 + -2x + (4x2) = x + -1x Combine like terms: x + -1x = 0 -4 + -2x + (4x2) = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -1x + (2x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -1x + (2x2))' equal to zero and attempt to solve: Simplifying -2 + -1x + (2x2) = 0 Solving -2 + -1x + (2x2) = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1 + -0.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.5x + x2 = 0 + 1 -0.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.5x + x2 = 1 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 1 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 1 + 0.0625 Combine like terms: 1 + 0.0625 = 1.0625 0.0625 + -0.5x + x2 = 1.0625 Factor a perfect square on the left side: ((x) + -0.25)((x) + -0.25) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting ((x) + -0.25) equal to 1.030776406 and -1.030776406.Subproblem 1
(x) + -0.25 = 1.030776406 Simplifying (x) + -0.25 = 1.030776406 x + -0.25 = 1.030776406 Reorder the terms: -0.25 + x = 1.030776406 Solving -0.25 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.030776406 + 0.25 x = 1.030776406 + 0.25 Combine like terms: 1.030776406 + 0.25 = 1.280776406 x = 1.280776406 Simplifying x = 1.280776406Subproblem 2
(x) + -0.25 = -1.030776406 Simplifying (x) + -0.25 = -1.030776406 x + -0.25 = -1.030776406 Reorder the terms: -0.25 + x = -1.030776406 Solving -0.25 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -1.030776406 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.030776406 + 0.25 x = -1.030776406 + 0.25 Combine like terms: -1.030776406 + 0.25 = -0.780776406 x = -0.780776406 Simplifying x = -0.780776406Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.280776406, -0.780776406}Solution
x = {1.280776406, -0.780776406}
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