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Simplifying 2x2 + 4x + 38 = -6 Reorder the terms: 38 + 4x + 2x2 = -6 Solving 38 + 4x + 2x2 = -6 Solving for variable 'x'. Reorder the terms: 38 + 6 + 4x + 2x2 = -6 + 6 Combine like terms: 38 + 6 = 44 44 + 4x + 2x2 = -6 + 6 Combine like terms: -6 + 6 = 0 44 + 4x + 2x2 = 0 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 = -21 1 + 2x + x2 = -21 Factor a perfect square on the left side: (x + 1)(x + 1) = -21 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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