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Simplifying 2x2 + 4x + -44 = 0 Reorder the terms: -44 + 4x + 2x2 = 0 Solving -44 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-22 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-22 + 2x + x2)' equal to zero and attempt to solve: Simplifying -22 + 2x + x2 = 0 Solving -22 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 2x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 2x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 2x + x2 = 0 + 22 2x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 2x + x2 = 22 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 22 + 1 Reorder the terms: 1 + 2x + x2 = 22 + 1 Combine like terms: 22 + 1 = 23 1 + 2x + x2 = 23 Factor a perfect square on the left side: (x + 1)(x + 1) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 1) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 1 = 4.795831523 Simplifying x + 1 = 4.795831523 Reorder the terms: 1 + x = 4.795831523 Solving 1 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 4.795831523 + -1 Combine like terms: 1 + -1 = 0 0 + x = 4.795831523 + -1 x = 4.795831523 + -1 Combine like terms: 4.795831523 + -1 = 3.795831523 x = 3.795831523 Simplifying x = 3.795831523Subproblem 2
x + 1 = -4.795831523 Simplifying x + 1 = -4.795831523 Reorder the terms: 1 + x = -4.795831523 Solving 1 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -4.795831523 + -1 Combine like terms: 1 + -1 = 0 0 + x = -4.795831523 + -1 x = -4.795831523 + -1 Combine like terms: -4.795831523 + -1 = -5.795831523 x = -5.795831523 Simplifying x = -5.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.795831523, -5.795831523}Solution
x = {3.795831523, -5.795831523}
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