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Simplifying 2x2 + 20x = -44 Reorder the terms: 20x + 2x2 = -44 Solving 20x + 2x2 = -44 Solving for variable 'x'. Reorder the terms: 44 + 20x + 2x2 = -44 + 44 Combine like terms: -44 + 44 = 0 44 + 20x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(22 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(22 + 10x + x2)' equal to zero and attempt to solve: Simplifying 22 + 10x + x2 = 0 Solving 22 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-22' to each side of the equation. 22 + 10x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + 10x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + 10x + x2 = 0 + -22 10x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 10x + x2 = -22 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -22 + 25 Reorder the terms: 25 + 10x + x2 = -22 + 25 Combine like terms: -22 + 25 = 3 25 + 10x + x2 = 3 Factor a perfect square on the left side: (x + 5)(x + 5) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 5) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 5 = 1.732050808 Simplifying x + 5 = 1.732050808 Reorder the terms: 5 + x = 1.732050808 Solving 5 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 1.732050808 + -5 Combine like terms: 5 + -5 = 0 0 + x = 1.732050808 + -5 x = 1.732050808 + -5 Combine like terms: 1.732050808 + -5 = -3.267949192 x = -3.267949192 Simplifying x = -3.267949192Subproblem 2
x + 5 = -1.732050808 Simplifying x + 5 = -1.732050808 Reorder the terms: 5 + x = -1.732050808 Solving 5 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -1.732050808 + -5 Combine like terms: 5 + -5 = 0 0 + x = -1.732050808 + -5 x = -1.732050808 + -5 Combine like terms: -1.732050808 + -5 = -6.732050808 x = -6.732050808 Simplifying x = -6.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.267949192, -6.732050808}Solution
x = {-3.267949192, -6.732050808}
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