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Simplifying 4x2 + 14x + 28 = 0 Reorder the terms: 28 + 14x + 4x2 = 0 Solving 28 + 14x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + 7x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying 14 + 7x + 2x2 = 0 Solving 14 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7 + 3.5x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 3.5x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 3.5x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3.5x + x2 = 0 + -7 3.5x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 3.5x + x2 = -7 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = -7 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -7 + 3.0625 Combine like terms: -7 + 3.0625 = -3.9375 3.0625 + 3.5x + x2 = -3.9375 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = -3.9375 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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