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Simplifying 0 = x2 + 2x + 420 Reorder the terms: 0 = 420 + 2x + x2 Solving 0 = 420 + 2x + x2 Solving for variable 'x'. Combine like terms: 0 + -420 = -420 -420 + -2x + -1x2 = 420 + 2x + x2 + -420 + -2x + -1x2 Reorder the terms: -420 + -2x + -1x2 = 420 + -420 + 2x + -2x + x2 + -1x2 Combine like terms: 420 + -420 = 0 -420 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 -420 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 -420 + -2x + -1x2 = 0 + x2 + -1x2 -420 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -420 + -2x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(420 + 2x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(420 + 2x + x2)' equal to zero and attempt to solve: Simplifying 420 + 2x + x2 = 0 Solving 420 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-420' to each side of the equation. 420 + 2x + -420 + x2 = 0 + -420 Reorder the terms: 420 + -420 + 2x + x2 = 0 + -420 Combine like terms: 420 + -420 = 0 0 + 2x + x2 = 0 + -420 2x + x2 = 0 + -420 Combine like terms: 0 + -420 = -420 2x + x2 = -420 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 = -420 + 1 Reorder the terms: 1 + 2x + x2 = -420 + 1 Combine like terms: -420 + 1 = -419 1 + 2x + x2 = -419 Factor a perfect square on the left side: (x + 1)(x + 1) = -419 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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