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Simplifying (0.8x2 + 0.5x + -0.9) + -1(0.9x2 + 1.3) = 0 Reorder the terms: (-0.9 + 0.5x + 0.8x2) + -1(0.9x2 + 1.3) = 0 Remove parenthesis around (-0.9 + 0.5x + 0.8x2) -0.9 + 0.5x + 0.8x2 + -1(0.9x2 + 1.3) = 0 Reorder the terms: -0.9 + 0.5x + 0.8x2 + -1(1.3 + 0.9x2) = 0 -0.9 + 0.5x + 0.8x2 + (1.3 * -1 + 0.9x2 * -1) = 0 -0.9 + 0.5x + 0.8x2 + (-1.3 + -0.9x2) = 0 Reorder the terms: -0.9 + -1.3 + 0.5x + 0.8x2 + -0.9x2 = 0 Combine like terms: -0.9 + -1.3 = -2.2 -2.2 + 0.5x + 0.8x2 + -0.9x2 = 0 Combine like terms: 0.8x2 + -0.9x2 = -0.1x2 -2.2 + 0.5x + -0.1x2 = 0 Solving -2.2 + 0.5x + -0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 22 + -5x + x2 = 0 Move the constant term to the right: Add '-22' to each side of the equation. 22 + -5x + -22 + x2 = 0 + -22 Reorder the terms: 22 + -22 + -5x + x2 = 0 + -22 Combine like terms: 22 + -22 = 0 0 + -5x + x2 = 0 + -22 -5x + x2 = 0 + -22 Combine like terms: 0 + -22 = -22 -5x + x2 = -22 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -22 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -22 + 6.25 Combine like terms: -22 + 6.25 = -15.75 6.25 + -5x + x2 = -15.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -15.75 Can't calculate square root of the right side. The solution to this equation could not be determined.
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