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Simplifying 4x + 1 = x2 + 20 + 100 Reorder the terms: 1 + 4x = x2 + 20 + 100 Reorder the terms: 1 + 4x = 20 + 100 + x2 Combine like terms: 20 + 100 = 120 1 + 4x = 120 + x2 Solving 1 + 4x = 120 + x2 Solving for variable 'x'. Reorder the terms: 1 + -120 + 4x + -1x2 = 120 + x2 + -120 + -1x2 Combine like terms: 1 + -120 = -119 -119 + 4x + -1x2 = 120 + x2 + -120 + -1x2 Reorder the terms: -119 + 4x + -1x2 = 120 + -120 + x2 + -1x2 Combine like terms: 120 + -120 = 0 -119 + 4x + -1x2 = 0 + x2 + -1x2 -119 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -119 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 119 + -4x + x2 = 0 Move the constant term to the right: Add '-119' to each side of the equation. 119 + -4x + -119 + x2 = 0 + -119 Reorder the terms: 119 + -119 + -4x + x2 = 0 + -119 Combine like terms: 119 + -119 = 0 0 + -4x + x2 = 0 + -119 -4x + x2 = 0 + -119 Combine like terms: 0 + -119 = -119 -4x + x2 = -119 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -119 + 4 Reorder the terms: 4 + -4x + x2 = -119 + 4 Combine like terms: -119 + 4 = -115 4 + -4x + x2 = -115 Factor a perfect square on the left side: (x + -2)(x + -2) = -115 Can't calculate square root of the right side. The solution to this equation could not be determined.
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