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Simplifying 12.98 = 0.5x2 + x + 24 Reorder the terms: 12.98 = 24 + x + 0.5x2 Solving 12.98 = 24 + x + 0.5x2 Solving for variable 'x'. Combine like terms: 12.98 + -24 = -11.02 -11.02 + -1x + -0.5x2 = 24 + x + 0.5x2 + -24 + -1x + -0.5x2 Reorder the terms: -11.02 + -1x + -0.5x2 = 24 + -24 + x + -1x + 0.5x2 + -0.5x2 Combine like terms: 24 + -24 = 0 -11.02 + -1x + -0.5x2 = 0 + x + -1x + 0.5x2 + -0.5x2 -11.02 + -1x + -0.5x2 = x + -1x + 0.5x2 + -0.5x2 Combine like terms: x + -1x = 0 -11.02 + -1x + -0.5x2 = 0 + 0.5x2 + -0.5x2 -11.02 + -1x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -11.02 + -1x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 22.04 + 2x + x2 = 0 Move the constant term to the right: Add '-22.04' to each side of the equation. 22.04 + 2x + -22.04 + x2 = 0 + -22.04 Reorder the terms: 22.04 + -22.04 + 2x + x2 = 0 + -22.04 Combine like terms: 22.04 + -22.04 = 0.00 0.00 + 2x + x2 = 0 + -22.04 2x + x2 = 0 + -22.04 Combine like terms: 0 + -22.04 = -22.04 2x + x2 = -22.04 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 = -22.04 + 1 Reorder the terms: 1 + 2x + x2 = -22.04 + 1 Combine like terms: -22.04 + 1 = -21.04 1 + 2x + x2 = -21.04 Factor a perfect square on the left side: (x + 1)(x + 1) = -21.04 Can't calculate square root of the right side. The solution to this equation could not be determined.
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