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Simplifying 4x2 + 8x + 14 = 0 Reorder the terms: 14 + 8x + 4x2 = 0 Solving 14 + 8x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 4x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying 7 + 4x + 2x2 = 0 Solving 7 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + 2x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 2x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 2x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 2x + x2 = 0 + -3.5 2x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 2x + x2 = -3.5 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 = -3.5 + 1 Reorder the terms: 1 + 2x + x2 = -3.5 + 1 Combine like terms: -3.5 + 1 = -2.5 1 + 2x + x2 = -2.5 Factor a perfect square on the left side: (x + 1)(x + 1) = -2.5 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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