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Simplifying 9x + -6 + 8x2 + -14 + 10x = 0 Reorder the terms: -6 + -14 + 9x + 10x + 8x2 = 0 Combine like terms: -6 + -14 = -20 -20 + 9x + 10x + 8x2 = 0 Combine like terms: 9x + 10x = 19x -20 + 19x + 8x2 = 0 Solving -20 + 19x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.5 + 2.375x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 2.375x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 2.375x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 2.375x + x2 = 0 + 2.5 2.375x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 2.375x + x2 = 2.5 The x term is 2.375x. Take half its coefficient (1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. 2.375x + 1.41015625 + x2 = 2.5 + 1.41015625 Reorder the terms: 1.41015625 + 2.375x + x2 = 2.5 + 1.41015625 Combine like terms: 2.5 + 1.41015625 = 3.91015625 1.41015625 + 2.375x + x2 = 3.91015625 Factor a perfect square on the left side: (x + 1.1875)(x + 1.1875) = 3.91015625 Calculate the square root of the right side: 1.977411502 Break this problem into two subproblems by setting (x + 1.1875) equal to 1.977411502 and -1.977411502.Subproblem 1
x + 1.1875 = 1.977411502 Simplifying x + 1.1875 = 1.977411502 Reorder the terms: 1.1875 + x = 1.977411502 Solving 1.1875 + x = 1.977411502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = 1.977411502 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = 1.977411502 + -1.1875 x = 1.977411502 + -1.1875 Combine like terms: 1.977411502 + -1.1875 = 0.789911502 x = 0.789911502 Simplifying x = 0.789911502Subproblem 2
x + 1.1875 = -1.977411502 Simplifying x + 1.1875 = -1.977411502 Reorder the terms: 1.1875 + x = -1.977411502 Solving 1.1875 + x = -1.977411502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = -1.977411502 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = -1.977411502 + -1.1875 x = -1.977411502 + -1.1875 Combine like terms: -1.977411502 + -1.1875 = -3.164911502 x = -3.164911502 Simplifying x = -3.164911502Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.789911502, -3.164911502}
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