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Simplifying 0 = x2 + 20x + 104 Reorder the terms: 0 = 104 + 20x + x2 Solving 0 = 104 + 20x + x2 Solving for variable 'x'. Combine like terms: 0 + -104 = -104 -104 + -20x + -1x2 = 104 + 20x + x2 + -104 + -20x + -1x2 Reorder the terms: -104 + -20x + -1x2 = 104 + -104 + 20x + -20x + x2 + -1x2 Combine like terms: 104 + -104 = 0 -104 + -20x + -1x2 = 0 + 20x + -20x + x2 + -1x2 -104 + -20x + -1x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 -104 + -20x + -1x2 = 0 + x2 + -1x2 -104 + -20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -104 + -20x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(104 + 20x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(104 + 20x + x2)' equal to zero and attempt to solve: Simplifying 104 + 20x + x2 = 0 Solving 104 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-104' to each side of the equation. 104 + 20x + -104 + x2 = 0 + -104 Reorder the terms: 104 + -104 + 20x + x2 = 0 + -104 Combine like terms: 104 + -104 = 0 0 + 20x + x2 = 0 + -104 20x + x2 = 0 + -104 Combine like terms: 0 + -104 = -104 20x + x2 = -104 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = -104 + 100 Reorder the terms: 100 + 20x + x2 = -104 + 100 Combine like terms: -104 + 100 = -4 100 + 20x + x2 = -4 Factor a perfect square on the left side: (x + 10)(x + 10) = -4 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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