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Simplifying 36x2 = -160 + -4x Solving 36x2 = -160 + -4x Solving for variable 'x'. Reorder the terms: 160 + 4x + 36x2 = -160 + -4x + 160 + 4x Reorder the terms: 160 + 4x + 36x2 = -160 + 160 + -4x + 4x Combine like terms: -160 + 160 = 0 160 + 4x + 36x2 = 0 + -4x + 4x 160 + 4x + 36x2 = -4x + 4x Combine like terms: -4x + 4x = 0 160 + 4x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(40 + x + 9x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(40 + x + 9x2)' equal to zero and attempt to solve: Simplifying 40 + x + 9x2 = 0 Solving 40 + x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 4.444444444 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '-4.444444444' to each side of the equation. 4.444444444 + 0.1111111111x + -4.444444444 + x2 = 0 + -4.444444444 Reorder the terms: 4.444444444 + -4.444444444 + 0.1111111111x + x2 = 0 + -4.444444444 Combine like terms: 4.444444444 + -4.444444444 = 0.000000000 0.000000000 + 0.1111111111x + x2 = 0 + -4.444444444 0.1111111111x + x2 = 0 + -4.444444444 Combine like terms: 0 + -4.444444444 = -4.444444444 0.1111111111x + x2 = -4.444444444 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1111111111x + 0.25 + x2 = -4.444444444 + 0.25 Reorder the terms: 0.25 + 0.1111111111x + x2 = -4.444444444 + 0.25 Combine like terms: -4.444444444 + 0.25 = -4.194444444 0.25 + 0.1111111111x + x2 = -4.194444444 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -4.194444444 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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