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Simplifying (-5x3 + 2x2 + -1x + 5) + -1(-5x3 + 3x2 + 5x + 3) = 0 Reorder the terms: (5 + -1x + 2x2 + -5x3) + -1(-5x3 + 3x2 + 5x + 3) = 0 Remove parenthesis around (5 + -1x + 2x2 + -5x3) 5 + -1x + 2x2 + -5x3 + -1(-5x3 + 3x2 + 5x + 3) = 0 Reorder the terms: 5 + -1x + 2x2 + -5x3 + -1(3 + 5x + 3x2 + -5x3) = 0 5 + -1x + 2x2 + -5x3 + (3 * -1 + 5x * -1 + 3x2 * -1 + -5x3 * -1) = 0 5 + -1x + 2x2 + -5x3 + (-3 + -5x + -3x2 + 5x3) = 0 Reorder the terms: 5 + -3 + -1x + -5x + 2x2 + -3x2 + -5x3 + 5x3 = 0 Combine like terms: 5 + -3 = 2 2 + -1x + -5x + 2x2 + -3x2 + -5x3 + 5x3 = 0 Combine like terms: -1x + -5x = -6x 2 + -6x + 2x2 + -3x2 + -5x3 + 5x3 = 0 Combine like terms: 2x2 + -3x2 = -1x2 2 + -6x + -1x2 + -5x3 + 5x3 = 0 Combine like terms: -5x3 + 5x3 = 0 2 + -6x + -1x2 + 0 = 0 2 + -6x + -1x2 = 0 Solving 2 + -6x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 6x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 6x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 6x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6x + x2 = 0 + 2 6x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 6x + x2 = 2 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 2 + 9 Reorder the terms: 9 + 6x + x2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + 6x + x2 = 11 Factor a perfect square on the left side: (x + 3)(x + 3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 3) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 3 = 3.31662479 Simplifying x + 3 = 3.31662479 Reorder the terms: 3 + x = 3.31662479 Solving 3 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.31662479 + -3 x = 3.31662479 + -3 Combine like terms: 3.31662479 + -3 = 0.31662479 x = 0.31662479 Simplifying x = 0.31662479Subproblem 2
x + 3 = -3.31662479 Simplifying x + 3 = -3.31662479 Reorder the terms: 3 + x = -3.31662479 Solving 3 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.31662479 + -3 x = -3.31662479 + -3 Combine like terms: -3.31662479 + -3 = -6.31662479 x = -6.31662479 Simplifying x = -6.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.31662479, -6.31662479}
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