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Simplifying 2x2 + -22 = -8x + 12 Reorder the terms: -22 + 2x2 = -8x + 12 Reorder the terms: -22 + 2x2 = 12 + -8x Solving -22 + 2x2 = 12 + -8x Solving for variable 'x'. Reorder the terms: -22 + -12 + 8x + 2x2 = 12 + -8x + -12 + 8x Combine like terms: -22 + -12 = -34 -34 + 8x + 2x2 = 12 + -8x + -12 + 8x Reorder the terms: -34 + 8x + 2x2 = 12 + -12 + -8x + 8x Combine like terms: 12 + -12 = 0 -34 + 8x + 2x2 = 0 + -8x + 8x -34 + 8x + 2x2 = -8x + 8x Combine like terms: -8x + 8x = 0 -34 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-17 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-17 + 4x + x2)' equal to zero and attempt to solve: Simplifying -17 + 4x + x2 = 0 Solving -17 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 4x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 4x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 4x + x2 = 0 + 17 4x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 4x + x2 = 17 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 17 + 4 Reorder the terms: 4 + 4x + x2 = 17 + 4 Combine like terms: 17 + 4 = 21 4 + 4x + x2 = 21 Factor a perfect square on the left side: (x + 2)(x + 2) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + 2) equal to 4.582575695 and -4.582575695.Subproblem 1
x + 2 = 4.582575695 Simplifying x + 2 = 4.582575695 Reorder the terms: 2 + x = 4.582575695 Solving 2 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 4.582575695 + -2 Combine like terms: 2 + -2 = 0 0 + x = 4.582575695 + -2 x = 4.582575695 + -2 Combine like terms: 4.582575695 + -2 = 2.582575695 x = 2.582575695 Simplifying x = 2.582575695Subproblem 2
x + 2 = -4.582575695 Simplifying x + 2 = -4.582575695 Reorder the terms: 2 + x = -4.582575695 Solving 2 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -4.582575695 + -2 Combine like terms: 2 + -2 = 0 0 + x = -4.582575695 + -2 x = -4.582575695 + -2 Combine like terms: -4.582575695 + -2 = -6.582575695 x = -6.582575695 Simplifying x = -6.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.582575695, -6.582575695}Solution
x = {2.582575695, -6.582575695}
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