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Simplifying 8x2 + 27x + -5 = 0 Reorder the terms: -5 + 27x + 8x2 = 0 Solving -5 + 27x + 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'. -0.625 + 3.375x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 3.375x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 3.375x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 3.375x + x2 = 0 + 0.625 3.375x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 3.375x + x2 = 0.625 The x term is 3.375x. Take half its coefficient (1.6875). Square it (2.84765625) and add it to both sides. Add '2.84765625' to each side of the equation. 3.375x + 2.84765625 + x2 = 0.625 + 2.84765625 Reorder the terms: 2.84765625 + 3.375x + x2 = 0.625 + 2.84765625 Combine like terms: 0.625 + 2.84765625 = 3.47265625 2.84765625 + 3.375x + x2 = 3.47265625 Factor a perfect square on the left side: (x + 1.6875)(x + 1.6875) = 3.47265625 Calculate the square root of the right side: 1.863506439 Break this problem into two subproblems by setting (x + 1.6875) equal to 1.863506439 and -1.863506439.Subproblem 1
x + 1.6875 = 1.863506439 Simplifying x + 1.6875 = 1.863506439 Reorder the terms: 1.6875 + x = 1.863506439 Solving 1.6875 + x = 1.863506439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6875' to each side of the equation. 1.6875 + -1.6875 + x = 1.863506439 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + x = 1.863506439 + -1.6875 x = 1.863506439 + -1.6875 Combine like terms: 1.863506439 + -1.6875 = 0.176006439 x = 0.176006439 Simplifying x = 0.176006439Subproblem 2
x + 1.6875 = -1.863506439 Simplifying x + 1.6875 = -1.863506439 Reorder the terms: 1.6875 + x = -1.863506439 Solving 1.6875 + x = -1.863506439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6875' to each side of the equation. 1.6875 + -1.6875 + x = -1.863506439 + -1.6875 Combine like terms: 1.6875 + -1.6875 = 0.0000 0.0000 + x = -1.863506439 + -1.6875 x = -1.863506439 + -1.6875 Combine like terms: -1.863506439 + -1.6875 = -3.551006439 x = -3.551006439 Simplifying x = -3.551006439Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.176006439, -3.551006439}
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