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Simplifying (8x2 + -5x + 16) + (6x2 + 9x + -77) = 0 Reorder the terms: (16 + -5x + 8x2) + (6x2 + 9x + -77) = 0 Remove parenthesis around (16 + -5x + 8x2) 16 + -5x + 8x2 + (6x2 + 9x + -77) = 0 Reorder the terms: 16 + -5x + 8x2 + (-77 + 9x + 6x2) = 0 Remove parenthesis around (-77 + 9x + 6x2) 16 + -5x + 8x2 + -77 + 9x + 6x2 = 0 Reorder the terms: 16 + -77 + -5x + 9x + 8x2 + 6x2 = 0 Combine like terms: 16 + -77 = -61 -61 + -5x + 9x + 8x2 + 6x2 = 0 Combine like terms: -5x + 9x = 4x -61 + 4x + 8x2 + 6x2 = 0 Combine like terms: 8x2 + 6x2 = 14x2 -61 + 4x + 14x2 = 0 Solving -61 + 4x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -4.357142857 + 0.2857142857x + x2 = 0 Move the constant term to the right: Add '4.357142857' to each side of the equation. -4.357142857 + 0.2857142857x + 4.357142857 + x2 = 0 + 4.357142857 Reorder the terms: -4.357142857 + 4.357142857 + 0.2857142857x + x2 = 0 + 4.357142857 Combine like terms: -4.357142857 + 4.357142857 = 0.000000000 0.000000000 + 0.2857142857x + x2 = 0 + 4.357142857 0.2857142857x + x2 = 0 + 4.357142857 Combine like terms: 0 + 4.357142857 = 4.357142857 0.2857142857x + x2 = 4.357142857 The x term is 0.2857142857x. Take half its coefficient (0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. 0.2857142857x + 0.02040816328 + x2 = 4.357142857 + 0.02040816328 Reorder the terms: 0.02040816328 + 0.2857142857x + x2 = 4.357142857 + 0.02040816328 Combine like terms: 4.357142857 + 0.02040816328 = 4.37755102028 0.02040816328 + 0.2857142857x + x2 = 4.37755102028 Factor a perfect square on the left side: (x + 0.1428571429)(x + 0.1428571429) = 4.37755102028 Calculate the square root of the right side: 2.092259788 Break this problem into two subproblems by setting (x + 0.1428571429) equal to 2.092259788 and -2.092259788.Subproblem 1
x + 0.1428571429 = 2.092259788 Simplifying x + 0.1428571429 = 2.092259788 Reorder the terms: 0.1428571429 + x = 2.092259788 Solving 0.1428571429 + x = 2.092259788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = 2.092259788 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = 2.092259788 + -0.1428571429 x = 2.092259788 + -0.1428571429 Combine like terms: 2.092259788 + -0.1428571429 = 1.9494026451 x = 1.9494026451 Simplifying x = 1.9494026451Subproblem 2
x + 0.1428571429 = -2.092259788 Simplifying x + 0.1428571429 = -2.092259788 Reorder the terms: 0.1428571429 + x = -2.092259788 Solving 0.1428571429 + x = -2.092259788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + x = -2.092259788 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + x = -2.092259788 + -0.1428571429 x = -2.092259788 + -0.1428571429 Combine like terms: -2.092259788 + -0.1428571429 = -2.2351169309 x = -2.2351169309 Simplifying x = -2.2351169309Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9494026451, -2.2351169309}
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