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Simplifying (3x2 + 2x + -1) + -1(5x2 + -1x + 2) + (4x2 + -5x + -6) = 0 Reorder the terms: (-1 + 2x + 3x2) + -1(5x2 + -1x + 2) + (4x2 + -5x + -6) = 0 Remove parenthesis around (-1 + 2x + 3x2) -1 + 2x + 3x2 + -1(5x2 + -1x + 2) + (4x2 + -5x + -6) = 0 Reorder the terms: -1 + 2x + 3x2 + -1(2 + -1x + 5x2) + (4x2 + -5x + -6) = 0 -1 + 2x + 3x2 + (2 * -1 + -1x * -1 + 5x2 * -1) + (4x2 + -5x + -6) = 0 -1 + 2x + 3x2 + (-2 + 1x + -5x2) + (4x2 + -5x + -6) = 0 Reorder the terms: -1 + 2x + 3x2 + -2 + 1x + -5x2 + (-6 + -5x + 4x2) = 0 Remove parenthesis around (-6 + -5x + 4x2) -1 + 2x + 3x2 + -2 + 1x + -5x2 + -6 + -5x + 4x2 = 0 Reorder the terms: -1 + -2 + -6 + 2x + 1x + -5x + 3x2 + -5x2 + 4x2 = 0 Combine like terms: -1 + -2 = -3 -3 + -6 + 2x + 1x + -5x + 3x2 + -5x2 + 4x2 = 0 Combine like terms: -3 + -6 = -9 -9 + 2x + 1x + -5x + 3x2 + -5x2 + 4x2 = 0 Combine like terms: 2x + 1x = 3x -9 + 3x + -5x + 3x2 + -5x2 + 4x2 = 0 Combine like terms: 3x + -5x = -2x -9 + -2x + 3x2 + -5x2 + 4x2 = 0 Combine like terms: 3x2 + -5x2 = -2x2 -9 + -2x + -2x2 + 4x2 = 0 Combine like terms: -2x2 + 4x2 = 2x2 -9 + -2x + 2x2 = 0 Solving -9 + -2x + 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'. -4.5 + -1x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -1x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -1x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -1x + x2 = 0 + 4.5 -1x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -1x + x2 = 4.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 4.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 4.5 + 0.25 Combine like terms: 4.5 + 0.25 = 4.75 0.25 + -1x + x2 = 4.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + -0.5) equal to 2.179449472 and -2.179449472.Subproblem 1
x + -0.5 = 2.179449472 Simplifying x + -0.5 = 2.179449472 Reorder the terms: -0.5 + x = 2.179449472 Solving -0.5 + x = 2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.179449472 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.179449472 + 0.5 x = 2.179449472 + 0.5 Combine like terms: 2.179449472 + 0.5 = 2.679449472 x = 2.679449472 Simplifying x = 2.679449472Subproblem 2
x + -0.5 = -2.179449472 Simplifying x + -0.5 = -2.179449472 Reorder the terms: -0.5 + x = -2.179449472 Solving -0.5 + x = -2.179449472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.179449472 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.179449472 + 0.5 x = -2.179449472 + 0.5 Combine like terms: -2.179449472 + 0.5 = -1.679449472 x = -1.679449472 Simplifying x = -1.679449472Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.679449472, -1.679449472}
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