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Simplifying 0.5 = x * x + 2x + 3 Multiply x * x 0.5 = x2 + 2x + 3 Reorder the terms: 0.5 = 3 + 2x + x2 Solving 0.5 = 3 + 2x + x2 Solving for variable 'x'. Combine like terms: 0.5 + -3 = -2.5 -2.5 + -2x + -1x2 = 3 + 2x + x2 + -3 + -2x + -1x2 Reorder the terms: -2.5 + -2x + -1x2 = 3 + -3 + 2x + -2x + x2 + -1x2 Combine like terms: 3 + -3 = 0 -2.5 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2 -2.5 + -2x + -1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 -2.5 + -2x + -1x2 = 0 + x2 + -1x2 -2.5 + -2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2.5 + -2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2.5 + 2x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 2x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 2x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 2x + x2 = 0 + -2.5 2x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 2x + x2 = -2.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -2.5 + 1 Reorder the terms: 1 + 2x + x2 = -2.5 + 1 Combine like terms: -2.5 + 1 = -1.5 1 + 2x + x2 = -1.5 Factor a perfect square on the left side: (x + 1)(x + 1) = -1.5 Can't calculate square root of the right side. The solution to this equation could not be determined.
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