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Simplifying 8x2 + 19x + -35 = 0 Reorder the terms: -35 + 19x + 8x2 = 0 Solving -35 + 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'. -4.375 + 2.375x + x2 = 0 Move the constant term to the right: Add '4.375' to each side of the equation. -4.375 + 2.375x + 4.375 + x2 = 0 + 4.375 Reorder the terms: -4.375 + 4.375 + 2.375x + x2 = 0 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + 2.375x + x2 = 0 + 4.375 2.375x + x2 = 0 + 4.375 Combine like terms: 0 + 4.375 = 4.375 2.375x + x2 = 4.375 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 = 4.375 + 1.41015625 Reorder the terms: 1.41015625 + 2.375x + x2 = 4.375 + 1.41015625 Combine like terms: 4.375 + 1.41015625 = 5.78515625 1.41015625 + 2.375x + x2 = 5.78515625 Factor a perfect square on the left side: (x + 1.1875)(x + 1.1875) = 5.78515625 Calculate the square root of the right side: 2.405235176 Break this problem into two subproblems by setting (x + 1.1875) equal to 2.405235176 and -2.405235176.Subproblem 1
x + 1.1875 = 2.405235176 Simplifying x + 1.1875 = 2.405235176 Reorder the terms: 1.1875 + x = 2.405235176 Solving 1.1875 + x = 2.405235176 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 = 2.405235176 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = 2.405235176 + -1.1875 x = 2.405235176 + -1.1875 Combine like terms: 2.405235176 + -1.1875 = 1.217735176 x = 1.217735176 Simplifying x = 1.217735176Subproblem 2
x + 1.1875 = -2.405235176 Simplifying x + 1.1875 = -2.405235176 Reorder the terms: 1.1875 + x = -2.405235176 Solving 1.1875 + x = -2.405235176 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 = -2.405235176 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = -2.405235176 + -1.1875 x = -2.405235176 + -1.1875 Combine like terms: -2.405235176 + -1.1875 = -3.592735176 x = -3.592735176 Simplifying x = -3.592735176Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.217735176, -3.592735176}
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