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Simplifying 0 = 2x2 + 22x + 320 Reorder the terms: 0 = 320 + 22x + 2x2 Solving 0 = 320 + 22x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -320 = -320 -320 + -22x + -2x2 = 320 + 22x + 2x2 + -320 + -22x + -2x2 Reorder the terms: -320 + -22x + -2x2 = 320 + -320 + 22x + -22x + 2x2 + -2x2 Combine like terms: 320 + -320 = 0 -320 + -22x + -2x2 = 0 + 22x + -22x + 2x2 + -2x2 -320 + -22x + -2x2 = 22x + -22x + 2x2 + -2x2 Combine like terms: 22x + -22x = 0 -320 + -22x + -2x2 = 0 + 2x2 + -2x2 -320 + -22x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -320 + -22x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(160 + 11x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(160 + 11x + x2)' equal to zero and attempt to solve: Simplifying 160 + 11x + x2 = 0 Solving 160 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-160' to each side of the equation. 160 + 11x + -160 + x2 = 0 + -160 Reorder the terms: 160 + -160 + 11x + x2 = 0 + -160 Combine like terms: 160 + -160 = 0 0 + 11x + x2 = 0 + -160 11x + x2 = 0 + -160 Combine like terms: 0 + -160 = -160 11x + x2 = -160 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = -160 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -160 + 30.25 Combine like terms: -160 + 30.25 = -129.75 30.25 + 11x + x2 = -129.75 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = -129.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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