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Simplifying 40x2 + 84x + 56 = 0 Reorder the terms: 56 + 84x + 40x2 = 0 Solving 56 + 84x + 40x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(14 + 21x + 10x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(14 + 21x + 10x2)' equal to zero and attempt to solve: Simplifying 14 + 21x + 10x2 = 0 Solving 14 + 21x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.4 + 2.1x + x2 = 0.0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 2.1x + -1.4 + x2 = 0.0 + -1.4 Reorder the terms: 1.4 + -1.4 + 2.1x + x2 = 0.0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 2.1x + x2 = 0.0 + -1.4 2.1x + x2 = 0.0 + -1.4 Combine like terms: 0.0 + -1.4 = -1.4 2.1x + x2 = -1.4 The x term is 2.1x. Take half its coefficient (1.05). Square it (1.1025) and add it to both sides. Add '1.1025' to each side of the equation. 2.1x + 1.1025 + x2 = -1.4 + 1.1025 Reorder the terms: 1.1025 + 2.1x + x2 = -1.4 + 1.1025 Combine like terms: -1.4 + 1.1025 = -0.2975 1.1025 + 2.1x + x2 = -0.2975 Factor a perfect square on the left side: (x + 1.05)(x + 1.05) = -0.2975 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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