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Simplifying (0.7x2 + 0.3x + -0.9) + -1(0.9x2 + 1.4) = 0 Reorder the terms: (-0.9 + 0.3x + 0.7x2) + -1(0.9x2 + 1.4) = 0 Remove parenthesis around (-0.9 + 0.3x + 0.7x2) -0.9 + 0.3x + 0.7x2 + -1(0.9x2 + 1.4) = 0 Reorder the terms: -0.9 + 0.3x + 0.7x2 + -1(1.4 + 0.9x2) = 0 -0.9 + 0.3x + 0.7x2 + (1.4 * -1 + 0.9x2 * -1) = 0 -0.9 + 0.3x + 0.7x2 + (-1.4 + -0.9x2) = 0 Reorder the terms: -0.9 + -1.4 + 0.3x + 0.7x2 + -0.9x2 = 0 Combine like terms: -0.9 + -1.4 = -2.3 -2.3 + 0.3x + 0.7x2 + -0.9x2 = 0 Combine like terms: 0.7x2 + -0.9x2 = -0.2x2 -2.3 + 0.3x + -0.2x2 = 0 Solving -2.3 + 0.3x + -0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.2 the coefficient of the squared term: Divide each side by '-0.2'. 11.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + -1.5x + -11.5 + x2 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + -1.5x + x2 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + -1.5x + x2 = 0 + -11.5 -1.5x + x2 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 -1.5x + x2 = -11.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -11.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -11.5 + 0.5625 Combine like terms: -11.5 + 0.5625 = -10.9375 0.5625 + -1.5x + x2 = -10.9375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -10.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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