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Simplifying (8x2 + -7x + 3) + (3x2 + x + -5) = 0 Reorder the terms: (3 + -7x + 8x2) + (3x2 + x + -5) = 0 Remove parenthesis around (3 + -7x + 8x2) 3 + -7x + 8x2 + (3x2 + x + -5) = 0 Reorder the terms: 3 + -7x + 8x2 + (-5 + x + 3x2) = 0 Remove parenthesis around (-5 + x + 3x2) 3 + -7x + 8x2 + -5 + x + 3x2 = 0 Reorder the terms: 3 + -5 + -7x + x + 8x2 + 3x2 = 0 Combine like terms: 3 + -5 = -2 -2 + -7x + x + 8x2 + 3x2 = 0 Combine like terms: -7x + x = -6x -2 + -6x + 8x2 + 3x2 = 0 Combine like terms: 8x2 + 3x2 = 11x2 -2 + -6x + 11x2 = 0 Solving -2 + -6x + 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'. -0.1818181818 + -0.5454545455x + x2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + -0.5454545455x + 0.1818181818 + x2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + -0.5454545455x + x2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + -0.5454545455x + x2 = 0 + 0.1818181818 -0.5454545455x + x2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 -0.5454545455x + x2 = 0.1818181818 The x term is -0.5454545455x. Take half its coefficient (-0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. -0.5454545455x + 0.07438016533 + x2 = 0.1818181818 + 0.07438016533 Reorder the terms: 0.07438016533 + -0.5454545455x + x2 = 0.1818181818 + 0.07438016533 Combine like terms: 0.1818181818 + 0.07438016533 = 0.25619834713 0.07438016533 + -0.5454545455x + x2 = 0.25619834713 Factor a perfect square on the left side: (x + -0.2727272728)(x + -0.2727272728) = 0.25619834713 Calculate the square root of the right side: 0.506160397 Break this problem into two subproblems by setting (x + -0.2727272728) equal to 0.506160397 and -0.506160397.Subproblem 1
x + -0.2727272728 = 0.506160397 Simplifying x + -0.2727272728 = 0.506160397 Reorder the terms: -0.2727272728 + x = 0.506160397 Solving -0.2727272728 + x = 0.506160397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = 0.506160397 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = 0.506160397 + 0.2727272728 x = 0.506160397 + 0.2727272728 Combine like terms: 0.506160397 + 0.2727272728 = 0.7788876698 x = 0.7788876698 Simplifying x = 0.7788876698Subproblem 2
x + -0.2727272728 = -0.506160397 Simplifying x + -0.2727272728 = -0.506160397 Reorder the terms: -0.2727272728 + x = -0.506160397 Solving -0.2727272728 + x = -0.506160397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2727272728' to each side of the equation. -0.2727272728 + 0.2727272728 + x = -0.506160397 + 0.2727272728 Combine like terms: -0.2727272728 + 0.2727272728 = 0.0000000000 0.0000000000 + x = -0.506160397 + 0.2727272728 x = -0.506160397 + 0.2727272728 Combine like terms: -0.506160397 + 0.2727272728 = -0.2334331242 x = -0.2334331242 Simplifying x = -0.2334331242Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7788876698, -0.2334331242}
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