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Simplifying 0.5x2 + 4x + 10 = x + 2 Reorder the terms: 10 + 4x + 0.5x2 = x + 2 Reorder the terms: 10 + 4x + 0.5x2 = 2 + x Solving 10 + 4x + 0.5x2 = 2 + x Solving for variable 'x'. Reorder the terms: 10 + -2 + 4x + -1x + 0.5x2 = 2 + x + -2 + -1x Combine like terms: 10 + -2 = 8 8 + 4x + -1x + 0.5x2 = 2 + x + -2 + -1x Combine like terms: 4x + -1x = 3x 8 + 3x + 0.5x2 = 2 + x + -2 + -1x Reorder the terms: 8 + 3x + 0.5x2 = 2 + -2 + x + -1x Combine like terms: 2 + -2 = 0 8 + 3x + 0.5x2 = 0 + x + -1x 8 + 3x + 0.5x2 = x + -1x Combine like terms: x + -1x = 0 8 + 3x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 16 + 6x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + 6x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 6x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 6x + x2 = 0 + -16 6x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 6x + x2 = -16 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -16 + 9 Reorder the terms: 9 + 6x + x2 = -16 + 9 Combine like terms: -16 + 9 = -7 9 + 6x + x2 = -7 Factor a perfect square on the left side: (x + 3)(x + 3) = -7 Can't calculate square root of the right side. The solution to this equation could not be determined.
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