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Simplifying (8x2 + -3x + -3) + (3x2 + -5x + -4) = 0 Reorder the terms: (-3 + -3x + 8x2) + (3x2 + -5x + -4) = 0 Remove parenthesis around (-3 + -3x + 8x2) -3 + -3x + 8x2 + (3x2 + -5x + -4) = 0 Reorder the terms: -3 + -3x + 8x2 + (-4 + -5x + 3x2) = 0 Remove parenthesis around (-4 + -5x + 3x2) -3 + -3x + 8x2 + -4 + -5x + 3x2 = 0 Reorder the terms: -3 + -4 + -3x + -5x + 8x2 + 3x2 = 0 Combine like terms: -3 + -4 = -7 -7 + -3x + -5x + 8x2 + 3x2 = 0 Combine like terms: -3x + -5x = -8x -7 + -8x + 8x2 + 3x2 = 0 Combine like terms: 8x2 + 3x2 = 11x2 -7 + -8x + 11x2 = 0 Solving -7 + -8x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.6363636364 + -0.7272727273x + x2 = 0 Move the constant term to the right: Add '0.6363636364' to each side of the equation. -0.6363636364 + -0.7272727273x + 0.6363636364 + x2 = 0 + 0.6363636364 Reorder the terms: -0.6363636364 + 0.6363636364 + -0.7272727273x + x2 = 0 + 0.6363636364 Combine like terms: -0.6363636364 + 0.6363636364 = 0.0000000000 0.0000000000 + -0.7272727273x + x2 = 0 + 0.6363636364 -0.7272727273x + x2 = 0 + 0.6363636364 Combine like terms: 0 + 0.6363636364 = 0.6363636364 -0.7272727273x + x2 = 0.6363636364 The x term is -0.7272727273x. Take half its coefficient (-0.3636363637). Square it (0.1322314050) and add it to both sides. Add '0.1322314050' to each side of the equation. -0.7272727273x + 0.1322314050 + x2 = 0.6363636364 + 0.1322314050 Reorder the terms: 0.1322314050 + -0.7272727273x + x2 = 0.6363636364 + 0.1322314050 Combine like terms: 0.6363636364 + 0.1322314050 = 0.7685950414 0.1322314050 + -0.7272727273x + x2 = 0.7685950414 Factor a perfect square on the left side: (x + -0.3636363637)(x + -0.3636363637) = 0.7685950414 Calculate the square root of the right side: 0.876695524 Break this problem into two subproblems by setting (x + -0.3636363637) equal to 0.876695524 and -0.876695524.Subproblem 1
x + -0.3636363637 = 0.876695524 Simplifying x + -0.3636363637 = 0.876695524 Reorder the terms: -0.3636363637 + x = 0.876695524 Solving -0.3636363637 + x = 0.876695524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = 0.876695524 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = 0.876695524 + 0.3636363637 x = 0.876695524 + 0.3636363637 Combine like terms: 0.876695524 + 0.3636363637 = 1.2403318877 x = 1.2403318877 Simplifying x = 1.2403318877Subproblem 2
x + -0.3636363637 = -0.876695524 Simplifying x + -0.3636363637 = -0.876695524 Reorder the terms: -0.3636363637 + x = -0.876695524 Solving -0.3636363637 + x = -0.876695524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3636363637' to each side of the equation. -0.3636363637 + 0.3636363637 + x = -0.876695524 + 0.3636363637 Combine like terms: -0.3636363637 + 0.3636363637 = 0.0000000000 0.0000000000 + x = -0.876695524 + 0.3636363637 x = -0.876695524 + 0.3636363637 Combine like terms: -0.876695524 + 0.3636363637 = -0.5130591603 x = -0.5130591603 Simplifying x = -0.5130591603Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2403318877, -0.5130591603}
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