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Simplifying 2x2 + 22x + 84 = 0 Reorder the terms: 84 + 22x + 2x2 = 0 Solving 84 + 22x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(42 + 11x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(42 + 11x + x2)' equal to zero and attempt to solve: Simplifying 42 + 11x + x2 = 0 Solving 42 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + 11x + -42 + x2 = 0 + -42 Reorder the terms: 42 + -42 + 11x + x2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + 11x + x2 = 0 + -42 11x + x2 = 0 + -42 Combine like terms: 0 + -42 = -42 11x + x2 = -42 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = -42 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -42 + 30.25 Combine like terms: -42 + 30.25 = -11.75 30.25 + 11x + x2 = -11.75 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = -11.75 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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