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Simplifying 9 + -2x(x + 4) + -10(25 + -1x + 4) = 5 + -3x + -4(x + 1) Reorder the terms: 9 + -2x(4 + x) + -10(25 + -1x + 4) = 5 + -3x + -4(x + 1) 9 + (4 * -2x + x * -2x) + -10(25 + -1x + 4) = 5 + -3x + -4(x + 1) 9 + (-8x + -2x2) + -10(25 + -1x + 4) = 5 + -3x + -4(x + 1) Reorder the terms: 9 + -8x + -2x2 + -10(25 + 4 + -1x) = 5 + -3x + -4(x + 1) Combine like terms: 25 + 4 = 29 9 + -8x + -2x2 + -10(29 + -1x) = 5 + -3x + -4(x + 1) 9 + -8x + -2x2 + (29 * -10 + -1x * -10) = 5 + -3x + -4(x + 1) 9 + -8x + -2x2 + (-290 + 10x) = 5 + -3x + -4(x + 1) Reorder the terms: 9 + -290 + -8x + 10x + -2x2 = 5 + -3x + -4(x + 1) Combine like terms: 9 + -290 = -281 -281 + -8x + 10x + -2x2 = 5 + -3x + -4(x + 1) Combine like terms: -8x + 10x = 2x -281 + 2x + -2x2 = 5 + -3x + -4(x + 1) Reorder the terms: -281 + 2x + -2x2 = 5 + -3x + -4(1 + x) -281 + 2x + -2x2 = 5 + -3x + (1 * -4 + x * -4) -281 + 2x + -2x2 = 5 + -3x + (-4 + -4x) Reorder the terms: -281 + 2x + -2x2 = 5 + -4 + -3x + -4x Combine like terms: 5 + -4 = 1 -281 + 2x + -2x2 = 1 + -3x + -4x Combine like terms: -3x + -4x = -7x -281 + 2x + -2x2 = 1 + -7x Solving -281 + 2x + -2x2 = 1 + -7x Solving for variable 'x'. Reorder the terms: -281 + -1 + 2x + 7x + -2x2 = 1 + -7x + -1 + 7x Combine like terms: -281 + -1 = -282 -282 + 2x + 7x + -2x2 = 1 + -7x + -1 + 7x Combine like terms: 2x + 7x = 9x -282 + 9x + -2x2 = 1 + -7x + -1 + 7x Reorder the terms: -282 + 9x + -2x2 = 1 + -1 + -7x + 7x Combine like terms: 1 + -1 = 0 -282 + 9x + -2x2 = 0 + -7x + 7x -282 + 9x + -2x2 = -7x + 7x Combine like terms: -7x + 7x = 0 -282 + 9x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 141 + -4.5x + x2 = 0 Move the constant term to the right: Add '-141' to each side of the equation. 141 + -4.5x + -141 + x2 = 0 + -141 Reorder the terms: 141 + -141 + -4.5x + x2 = 0 + -141 Combine like terms: 141 + -141 = 0 0 + -4.5x + x2 = 0 + -141 -4.5x + x2 = 0 + -141 Combine like terms: 0 + -141 = -141 -4.5x + x2 = -141 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -141 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -141 + 5.0625 Combine like terms: -141 + 5.0625 = -135.9375 5.0625 + -4.5x + x2 = -135.9375 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = -135.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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