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Simplifying 2x2 + 12x + 52 = 0 Reorder the terms: 52 + 12x + 2x2 = 0 Solving 52 + 12x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(26 + 6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(26 + 6x + x2)' equal to zero and attempt to solve: Simplifying 26 + 6x + x2 = 0 Solving 26 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + 6x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + 6x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + 6x + x2 = 0 + -26 6x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 6x + x2 = -26 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -26 + 9 Reorder the terms: 9 + 6x + x2 = -26 + 9 Combine like terms: -26 + 9 = -17 9 + 6x + x2 = -17 Factor a perfect square on the left side: (x + 3)(x + 3) = -17 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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