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Simplifying 16x2 + 32x + 46 = 0 Reorder the terms: 46 + 32x + 16x2 = 0 Solving 46 + 32x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(23 + 16x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(23 + 16x + 8x2)' equal to zero and attempt to solve: Simplifying 23 + 16x + 8x2 = 0 Solving 23 + 16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.875 + 2x + x2 = 0 Move the constant term to the right: Add '-2.875' to each side of the equation. 2.875 + 2x + -2.875 + x2 = 0 + -2.875 Reorder the terms: 2.875 + -2.875 + 2x + x2 = 0 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + 2x + x2 = 0 + -2.875 2x + x2 = 0 + -2.875 Combine like terms: 0 + -2.875 = -2.875 2x + x2 = -2.875 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 = -2.875 + 1 Reorder the terms: 1 + 2x + x2 = -2.875 + 1 Combine like terms: -2.875 + 1 = -1.875 1 + 2x + x2 = -1.875 Factor a perfect square on the left side: (x + 1)(x + 1) = -1.875 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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