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Simplifying 0 = (2x2 + 4x + -7) + -1(9x2 + -5x + 4) Reorder the terms: 0 = (-7 + 4x + 2x2) + -1(9x2 + -5x + 4) Remove parenthesis around (-7 + 4x + 2x2) 0 = -7 + 4x + 2x2 + -1(9x2 + -5x + 4) Reorder the terms: 0 = -7 + 4x + 2x2 + -1(4 + -5x + 9x2) 0 = -7 + 4x + 2x2 + (4 * -1 + -5x * -1 + 9x2 * -1) 0 = -7 + 4x + 2x2 + (-4 + 5x + -9x2) Reorder the terms: 0 = -7 + -4 + 4x + 5x + 2x2 + -9x2 Combine like terms: -7 + -4 = -11 0 = -11 + 4x + 5x + 2x2 + -9x2 Combine like terms: 4x + 5x = 9x 0 = -11 + 9x + 2x2 + -9x2 Combine like terms: 2x2 + -9x2 = -7x2 0 = -11 + 9x + -7x2 Solving 0 = -11 + 9x + -7x2 Solving for variable 'x'. Combine like terms: 0 + 11 = 11 11 + -9x + 7x2 = -11 + 9x + -7x2 + 11 + -9x + 7x2 Reorder the terms: 11 + -9x + 7x2 = -11 + 11 + 9x + -9x + -7x2 + 7x2 Combine like terms: -11 + 11 = 0 11 + -9x + 7x2 = 0 + 9x + -9x + -7x2 + 7x2 11 + -9x + 7x2 = 9x + -9x + -7x2 + 7x2 Combine like terms: 9x + -9x = 0 11 + -9x + 7x2 = 0 + -7x2 + 7x2 11 + -9x + 7x2 = -7x2 + 7x2 Combine like terms: -7x2 + 7x2 = 0 11 + -9x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.571428571 + -1.285714286x + x2 = 0 Move the constant term to the right: Add '-1.571428571' to each side of the equation. 1.571428571 + -1.285714286x + -1.571428571 + x2 = 0 + -1.571428571 Reorder the terms: 1.571428571 + -1.571428571 + -1.285714286x + x2 = 0 + -1.571428571 Combine like terms: 1.571428571 + -1.571428571 = 0.000000000 0.000000000 + -1.285714286x + x2 = 0 + -1.571428571 -1.285714286x + x2 = 0 + -1.571428571 Combine like terms: 0 + -1.571428571 = -1.571428571 -1.285714286x + x2 = -1.571428571 The x term is -1.285714286x. Take half its coefficient (-0.642857143). Square it (0.4132653063) and add it to both sides. Add '0.4132653063' to each side of the equation. -1.285714286x + 0.4132653063 + x2 = -1.571428571 + 0.4132653063 Reorder the terms: 0.4132653063 + -1.285714286x + x2 = -1.571428571 + 0.4132653063 Combine like terms: -1.571428571 + 0.4132653063 = -1.1581632647 0.4132653063 + -1.285714286x + x2 = -1.1581632647 Factor a perfect square on the left side: (x + -0.642857143)(x + -0.642857143) = -1.1581632647 Can't calculate square root of the right side. The solution to this equation could not be determined.
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