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Simplifying 5 = -4x2 + -14x + -9 Reorder the terms: 5 = -9 + -14x + -4x2 Solving 5 = -9 + -14x + -4x2 Solving for variable 'x'. Combine like terms: 5 + 9 = 14 14 + 14x + 4x2 = -9 + -14x + -4x2 + 9 + 14x + 4x2 Reorder the terms: 14 + 14x + 4x2 = -9 + 9 + -14x + 14x + -4x2 + 4x2 Combine like terms: -9 + 9 = 0 14 + 14x + 4x2 = 0 + -14x + 14x + -4x2 + 4x2 14 + 14x + 4x2 = -14x + 14x + -4x2 + 4x2 Combine like terms: -14x + 14x = 0 14 + 14x + 4x2 = 0 + -4x2 + 4x2 14 + 14x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 14 + 14x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(7 + 7x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + 7x + 2x2)' equal to zero and attempt to solve: Simplifying 7 + 7x + 2x2 = 0 Solving 7 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + 3.5x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + 3.5x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + 3.5x + x2 = 0 + -3.5 3.5x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 3.5x + x2 = -3.5 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 = -3.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = -3.5 + 3.0625 Combine like terms: -3.5 + 3.0625 = -0.4375 3.0625 + 3.5x + x2 = -0.4375 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = -0.4375 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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