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Simplifying 0 = 4x2 + 44x + 160 Reorder the terms: 0 = 160 + 44x + 4x2 Solving 0 = 160 + 44x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -160 = -160 -160 + -44x + -4x2 = 160 + 44x + 4x2 + -160 + -44x + -4x2 Reorder the terms: -160 + -44x + -4x2 = 160 + -160 + 44x + -44x + 4x2 + -4x2 Combine like terms: 160 + -160 = 0 -160 + -44x + -4x2 = 0 + 44x + -44x + 4x2 + -4x2 -160 + -44x + -4x2 = 44x + -44x + 4x2 + -4x2 Combine like terms: 44x + -44x = 0 -160 + -44x + -4x2 = 0 + 4x2 + -4x2 -160 + -44x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -160 + -44x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-4'. -4(40 + 11x + x2) = 0 Ignore the factor -4.Subproblem 1
Set the factor '(40 + 11x + x2)' equal to zero and attempt to solve: Simplifying 40 + 11x + x2 = 0 Solving 40 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 11x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + 11x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 11x + x2 = 0 + -40 11x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 11x + x2 = -40 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = -40 + 30.25 Reorder the terms: 30.25 + 11x + x2 = -40 + 30.25 Combine like terms: -40 + 30.25 = -9.75 30.25 + 11x + x2 = -9.75 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = -9.75 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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