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Simplifying x(x + -5) = 2x(x + -7) + 5(x + 9) Reorder the terms: x(-5 + x) = 2x(x + -7) + 5(x + 9) (-5 * x + x * x) = 2x(x + -7) + 5(x + 9) (-5x + x2) = 2x(x + -7) + 5(x + 9) Reorder the terms: -5x + x2 = 2x(-7 + x) + 5(x + 9) -5x + x2 = (-7 * 2x + x * 2x) + 5(x + 9) -5x + x2 = (-14x + 2x2) + 5(x + 9) Reorder the terms: -5x + x2 = -14x + 2x2 + 5(9 + x) -5x + x2 = -14x + 2x2 + (9 * 5 + x * 5) -5x + x2 = -14x + 2x2 + (45 + 5x) Reorder the terms: -5x + x2 = 45 + -14x + 5x + 2x2 Combine like terms: -14x + 5x = -9x -5x + x2 = 45 + -9x + 2x2 Solving -5x + x2 = 45 + -9x + 2x2 Solving for variable 'x'. Reorder the terms: -45 + -5x + 9x + x2 + -2x2 = 45 + -9x + 2x2 + -45 + 9x + -2x2 Combine like terms: -5x + 9x = 4x -45 + 4x + x2 + -2x2 = 45 + -9x + 2x2 + -45 + 9x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -45 + 4x + -1x2 = 45 + -9x + 2x2 + -45 + 9x + -2x2 Reorder the terms: -45 + 4x + -1x2 = 45 + -45 + -9x + 9x + 2x2 + -2x2 Combine like terms: 45 + -45 = 0 -45 + 4x + -1x2 = 0 + -9x + 9x + 2x2 + -2x2 -45 + 4x + -1x2 = -9x + 9x + 2x2 + -2x2 Combine like terms: -9x + 9x = 0 -45 + 4x + -1x2 = 0 + 2x2 + -2x2 -45 + 4x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -45 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 45 + -4x + x2 = 0 Move the constant term to the right: Add '-45' to each side of the equation. 45 + -4x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + -4x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -4x + x2 = 0 + -45 -4x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 -4x + x2 = -45 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -45 + 4 Reorder the terms: 4 + -4x + x2 = -45 + 4 Combine like terms: -45 + 4 = -41 4 + -4x + x2 = -41 Factor a perfect square on the left side: (x + -2)(x + -2) = -41 Can't calculate square root of the right side. The solution to this equation could not be determined.
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