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Simplifying 4x2 + -3x + -9 + -1(2x2 + 22x + 27) = 0 Reorder the terms: 4x2 + -3x + -9 + -1(27 + 22x + 2x2) = 0 4x2 + -3x + -9 + (27 * -1 + 22x * -1 + 2x2 * -1) = 0 4x2 + -3x + -9 + (-27 + -22x + -2x2) = 0 Reorder the terms: -9 + -27 + -3x + -22x + 4x2 + -2x2 = 0 Combine like terms: -9 + -27 = -36 -36 + -3x + -22x + 4x2 + -2x2 = 0 Combine like terms: -3x + -22x = -25x -36 + -25x + 4x2 + -2x2 = 0 Combine like terms: 4x2 + -2x2 = 2x2 -36 + -25x + 2x2 = 0 Solving -36 + -25x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -18 + -12.5x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -12.5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -12.5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -12.5x + x2 = 0 + 18 -12.5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -12.5x + x2 = 18 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 18 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 18 + 39.0625 Combine like terms: 18 + 39.0625 = 57.0625 39.0625 + -12.5x + x2 = 57.0625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 57.0625 Calculate the square root of the right side: 7.553972465 Break this problem into two subproblems by setting (x + -6.25) equal to 7.553972465 and -7.553972465.Subproblem 1
x + -6.25 = 7.553972465 Simplifying x + -6.25 = 7.553972465 Reorder the terms: -6.25 + x = 7.553972465 Solving -6.25 + x = 7.553972465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 7.553972465 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 7.553972465 + 6.25 x = 7.553972465 + 6.25 Combine like terms: 7.553972465 + 6.25 = 13.803972465 x = 13.803972465 Simplifying x = 13.803972465Subproblem 2
x + -6.25 = -7.553972465 Simplifying x + -6.25 = -7.553972465 Reorder the terms: -6.25 + x = -7.553972465 Solving -6.25 + x = -7.553972465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -7.553972465 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -7.553972465 + 6.25 x = -7.553972465 + 6.25 Combine like terms: -7.553972465 + 6.25 = -1.303972465 x = -1.303972465 Simplifying x = -1.303972465Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.803972465, -1.303972465}
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