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Simplifying (x2 + -3x + -5) + -1(-4x2 + 8x + 9) = 0 Reorder the terms: (-5 + -3x + x2) + -1(-4x2 + 8x + 9) = 0 Remove parenthesis around (-5 + -3x + x2) -5 + -3x + x2 + -1(-4x2 + 8x + 9) = 0 Reorder the terms: -5 + -3x + x2 + -1(9 + 8x + -4x2) = 0 -5 + -3x + x2 + (9 * -1 + 8x * -1 + -4x2 * -1) = 0 -5 + -3x + x2 + (-9 + -8x + 4x2) = 0 Reorder the terms: -5 + -9 + -3x + -8x + x2 + 4x2 = 0 Combine like terms: -5 + -9 = -14 -14 + -3x + -8x + x2 + 4x2 = 0 Combine like terms: -3x + -8x = -11x -14 + -11x + x2 + 4x2 = 0 Combine like terms: x2 + 4x2 = 5x2 -14 + -11x + 5x2 = 0 Solving -14 + -11x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.8 + -2.2x + x2 = 0 Move the constant term to the right: Add '2.8' to each side of the equation. -2.8 + -2.2x + 2.8 + x2 = 0 + 2.8 Reorder the terms: -2.8 + 2.8 + -2.2x + x2 = 0 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + -2.2x + x2 = 0 + 2.8 -2.2x + x2 = 0 + 2.8 Combine like terms: 0 + 2.8 = 2.8 -2.2x + x2 = 2.8 The x term is -2.2x. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2x + 1.21 + x2 = 2.8 + 1.21 Reorder the terms: 1.21 + -2.2x + x2 = 2.8 + 1.21 Combine like terms: 2.8 + 1.21 = 4.01 1.21 + -2.2x + x2 = 4.01 Factor a perfect square on the left side: (x + -1.1)(x + -1.1) = 4.01 Calculate the square root of the right side: 2.002498439 Break this problem into two subproblems by setting (x + -1.1) equal to 2.002498439 and -2.002498439.Subproblem 1
x + -1.1 = 2.002498439 Simplifying x + -1.1 = 2.002498439 Reorder the terms: -1.1 + x = 2.002498439 Solving -1.1 + x = 2.002498439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = 2.002498439 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = 2.002498439 + 1.1 x = 2.002498439 + 1.1 Combine like terms: 2.002498439 + 1.1 = 3.102498439 x = 3.102498439 Simplifying x = 3.102498439Subproblem 2
x + -1.1 = -2.002498439 Simplifying x + -1.1 = -2.002498439 Reorder the terms: -1.1 + x = -2.002498439 Solving -1.1 + x = -2.002498439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + x = -2.002498439 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + x = -2.002498439 + 1.1 x = -2.002498439 + 1.1 Combine like terms: -2.002498439 + 1.1 = -0.902498439 x = -0.902498439 Simplifying x = -0.902498439Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.102498439, -0.902498439}
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