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Simplifying 2x2 + 2x = -74 Reorder the terms: 2x + 2x2 = -74 Solving 2x + 2x2 = -74 Solving for variable 'x'. Reorder the terms: 74 + 2x + 2x2 = -74 + 74 Combine like terms: -74 + 74 = 0 74 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(37 + x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(37 + x + x2)' equal to zero and attempt to solve: Simplifying 37 + x + x2 = 0 Solving 37 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + x + x2 = 0 + -37 x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 x + x2 = -37 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = -37 + 0.25 Reorder the terms: 0.25 + x + x2 = -37 + 0.25 Combine like terms: -37 + 0.25 = -36.75 0.25 + x + x2 = -36.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -36.75 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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