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Simplifying 8x2 + 19x + -50 = 0 Reorder the terms: -50 + 19x + 8x2 = 0 Solving -50 + 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'. -6.25 + 2.375x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 2.375x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 2.375x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 2.375x + x2 = 0 + 6.25 2.375x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 2.375x + x2 = 6.25 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 = 6.25 + 1.41015625 Reorder the terms: 1.41015625 + 2.375x + x2 = 6.25 + 1.41015625 Combine like terms: 6.25 + 1.41015625 = 7.66015625 1.41015625 + 2.375x + x2 = 7.66015625 Factor a perfect square on the left side: (x + 1.1875)(x + 1.1875) = 7.66015625 Calculate the square root of the right side: 2.767698728 Break this problem into two subproblems by setting (x + 1.1875) equal to 2.767698728 and -2.767698728.Subproblem 1
x + 1.1875 = 2.767698728 Simplifying x + 1.1875 = 2.767698728 Reorder the terms: 1.1875 + x = 2.767698728 Solving 1.1875 + x = 2.767698728 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 = 2.767698728 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = 2.767698728 + -1.1875 x = 2.767698728 + -1.1875 Combine like terms: 2.767698728 + -1.1875 = 1.580198728 x = 1.580198728 Simplifying x = 1.580198728Subproblem 2
x + 1.1875 = -2.767698728 Simplifying x + 1.1875 = -2.767698728 Reorder the terms: 1.1875 + x = -2.767698728 Solving 1.1875 + x = -2.767698728 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 = -2.767698728 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = -2.767698728 + -1.1875 x = -2.767698728 + -1.1875 Combine like terms: -2.767698728 + -1.1875 = -3.955198728 x = -3.955198728 Simplifying x = -3.955198728Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.580198728, -3.955198728}
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