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Simplifying (3x2 + -7x + 14) + 8x2 + 9x + -89 = 0 Reorder the terms: (14 + -7x + 3x2) + 8x2 + 9x + -89 = 0 Remove parenthesis around (14 + -7x + 3x2) 14 + -7x + 3x2 + 8x2 + 9x + -89 = 0 Reorder the terms: 14 + -89 + -7x + 9x + 3x2 + 8x2 = 0 Combine like terms: 14 + -89 = -75 -75 + -7x + 9x + 3x2 + 8x2 = 0 Combine like terms: -7x + 9x = 2x -75 + 2x + 3x2 + 8x2 = 0 Combine like terms: 3x2 + 8x2 = 11x2 -75 + 2x + 11x2 = 0 Solving -75 + 2x + 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'. -6.818181818 + 0.1818181818x + x2 = 0 Move the constant term to the right: Add '6.818181818' to each side of the equation. -6.818181818 + 0.1818181818x + 6.818181818 + x2 = 0 + 6.818181818 Reorder the terms: -6.818181818 + 6.818181818 + 0.1818181818x + x2 = 0 + 6.818181818 Combine like terms: -6.818181818 + 6.818181818 = 0.000000000 0.000000000 + 0.1818181818x + x2 = 0 + 6.818181818 0.1818181818x + x2 = 0 + 6.818181818 Combine like terms: 0 + 6.818181818 = 6.818181818 0.1818181818x + x2 = 6.818181818 The x term is 0.1818181818x. Take half its coefficient (0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. 0.1818181818x + 0.008264462808 + x2 = 6.818181818 + 0.008264462808 Reorder the terms: 0.008264462808 + 0.1818181818x + x2 = 6.818181818 + 0.008264462808 Combine like terms: 6.818181818 + 0.008264462808 = 6.826446280808 0.008264462808 + 0.1818181818x + x2 = 6.826446280808 Factor a perfect square on the left side: (x + 0.0909090909)(x + 0.0909090909) = 6.826446280808 Calculate the square root of the right side: 2.612746884 Break this problem into two subproblems by setting (x + 0.0909090909) equal to 2.612746884 and -2.612746884.Subproblem 1
x + 0.0909090909 = 2.612746884 Simplifying x + 0.0909090909 = 2.612746884 Reorder the terms: 0.0909090909 + x = 2.612746884 Solving 0.0909090909 + x = 2.612746884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = 2.612746884 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = 2.612746884 + -0.0909090909 x = 2.612746884 + -0.0909090909 Combine like terms: 2.612746884 + -0.0909090909 = 2.5218377931 x = 2.5218377931 Simplifying x = 2.5218377931Subproblem 2
x + 0.0909090909 = -2.612746884 Simplifying x + 0.0909090909 = -2.612746884 Reorder the terms: 0.0909090909 + x = -2.612746884 Solving 0.0909090909 + x = -2.612746884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0909090909' to each side of the equation. 0.0909090909 + -0.0909090909 + x = -2.612746884 + -0.0909090909 Combine like terms: 0.0909090909 + -0.0909090909 = 0.0000000000 0.0000000000 + x = -2.612746884 + -0.0909090909 x = -2.612746884 + -0.0909090909 Combine like terms: -2.612746884 + -0.0909090909 = -2.7036559749 x = -2.7036559749 Simplifying x = -2.7036559749Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5218377931, -2.7036559749}
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