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Simplifying 2x2 + 14x + 38 = 0 Reorder the terms: 38 + 14x + 2x2 = 0 Solving 38 + 14x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(19 + 7x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + 7x + x2)' equal to zero and attempt to solve: Simplifying 19 + 7x + x2 = 0 Solving 19 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 7x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + 7x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 7x + x2 = 0 + -19 7x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 7x + x2 = -19 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -19 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -19 + 12.25 Combine like terms: -19 + 12.25 = -6.75 12.25 + 7x + x2 = -6.75 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -6.75 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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