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Simplifying 2x2 + 4x + -220 = 0 Reorder the terms: -220 + 4x + 2x2 = 0 Solving -220 + 4x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-110 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-110 + 2x + x2)' equal to zero and attempt to solve: Simplifying -110 + 2x + x2 = 0 Solving -110 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '110' to each side of the equation. -110 + 2x + 110 + x2 = 0 + 110 Reorder the terms: -110 + 110 + 2x + x2 = 0 + 110 Combine like terms: -110 + 110 = 0 0 + 2x + x2 = 0 + 110 2x + x2 = 0 + 110 Combine like terms: 0 + 110 = 110 2x + x2 = 110 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 = 110 + 1 Reorder the terms: 1 + 2x + x2 = 110 + 1 Combine like terms: 110 + 1 = 111 1 + 2x + x2 = 111 Factor a perfect square on the left side: (x + 1)(x + 1) = 111 Calculate the square root of the right side: 10.535653753 Break this problem into two subproblems by setting (x + 1) equal to 10.535653753 and -10.535653753.Subproblem 1
x + 1 = 10.535653753 Simplifying x + 1 = 10.535653753 Reorder the terms: 1 + x = 10.535653753 Solving 1 + x = 10.535653753 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 = 10.535653753 + -1 Combine like terms: 1 + -1 = 0 0 + x = 10.535653753 + -1 x = 10.535653753 + -1 Combine like terms: 10.535653753 + -1 = 9.535653753 x = 9.535653753 Simplifying x = 9.535653753Subproblem 2
x + 1 = -10.535653753 Simplifying x + 1 = -10.535653753 Reorder the terms: 1 + x = -10.535653753 Solving 1 + x = -10.535653753 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 = -10.535653753 + -1 Combine like terms: 1 + -1 = 0 0 + x = -10.535653753 + -1 x = -10.535653753 + -1 Combine like terms: -10.535653753 + -1 = -11.535653753 x = -11.535653753 Simplifying x = -11.535653753Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.535653753, -11.535653753}Solution
x = {9.535653753, -11.535653753}
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