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Simplifying x2 + 2x + 100 = x + 52 Reorder the terms: 100 + 2x + x2 = x + 52 Reorder the terms: 100 + 2x + x2 = 52 + x Solving 100 + 2x + x2 = 52 + x Solving for variable 'x'. Reorder the terms: 100 + -52 + 2x + -1x + x2 = 52 + x + -52 + -1x Combine like terms: 100 + -52 = 48 48 + 2x + -1x + x2 = 52 + x + -52 + -1x Combine like terms: 2x + -1x = 1x 48 + 1x + x2 = 52 + x + -52 + -1x Reorder the terms: 48 + 1x + x2 = 52 + -52 + x + -1x Combine like terms: 52 + -52 = 0 48 + 1x + x2 = 0 + x + -1x 48 + 1x + x2 = x + -1x Combine like terms: x + -1x = 0 48 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-48' to each side of the equation. 48 + 1x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + 1x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + 1x + x2 = 0 + -48 1x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 1x + x2 = -48 The x term is 1x. 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. x + 0.25 + x2 = -48 + 0.25 Reorder the terms: 0.25 + x + x2 = -48 + 0.25 Combine like terms: -48 + 0.25 = -47.75 0.25 + x + x2 = -47.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -47.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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