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Simplifying 80x2 + 32x + 56 = 0 Reorder the terms: 56 + 32x + 80x2 = 0 Solving 56 + 32x + 80x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(7 + 4x + 10x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(7 + 4x + 10x2)' equal to zero and attempt to solve: Simplifying 7 + 4x + 10x2 = 0 Solving 7 + 4x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.7 + 0.4x + x2 = 0.0 Move the constant term to the right: Add '-0.7' to each side of the equation. 0.7 + 0.4x + -0.7 + x2 = 0.0 + -0.7 Reorder the terms: 0.7 + -0.7 + 0.4x + x2 = 0.0 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + 0.4x + x2 = 0.0 + -0.7 0.4x + x2 = 0.0 + -0.7 Combine like terms: 0.0 + -0.7 = -0.7 0.4x + x2 = -0.7 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = -0.7 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = -0.7 + 0.04 Combine like terms: -0.7 + 0.04 = -0.66 0.04 + 0.4x + x2 = -0.66 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = -0.66 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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