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Simplifying 8x2 + 19x + 4 = 0 Reorder the terms: 4 + 19x + 8x2 = 0 Solving 4 + 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'. 0.5 + 2.375x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 2.375x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 2.375x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 2.375x + x2 = 0 + -0.5 2.375x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 2.375x + x2 = -0.5 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 = -0.5 + 1.41015625 Reorder the terms: 1.41015625 + 2.375x + x2 = -0.5 + 1.41015625 Combine like terms: -0.5 + 1.41015625 = 0.91015625 1.41015625 + 2.375x + x2 = 0.91015625 Factor a perfect square on the left side: (x + 1.1875)(x + 1.1875) = 0.91015625 Calculate the square root of the right side: 0.954021095 Break this problem into two subproblems by setting (x + 1.1875) equal to 0.954021095 and -0.954021095.Subproblem 1
x + 1.1875 = 0.954021095 Simplifying x + 1.1875 = 0.954021095 Reorder the terms: 1.1875 + x = 0.954021095 Solving 1.1875 + x = 0.954021095 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 = 0.954021095 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = 0.954021095 + -1.1875 x = 0.954021095 + -1.1875 Combine like terms: 0.954021095 + -1.1875 = -0.233478905 x = -0.233478905 Simplifying x = -0.233478905Subproblem 2
x + 1.1875 = -0.954021095 Simplifying x + 1.1875 = -0.954021095 Reorder the terms: 1.1875 + x = -0.954021095 Solving 1.1875 + x = -0.954021095 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 = -0.954021095 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = -0.954021095 + -1.1875 x = -0.954021095 + -1.1875 Combine like terms: -0.954021095 + -1.1875 = -2.141521095 x = -2.141521095 Simplifying x = -2.141521095Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.233478905, -2.141521095}
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