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Simplifying 8x2 + -5x = 11 Reorder the terms: -5x + 8x2 = 11 Solving -5x + 8x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -5x + 8x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.375 + -0.625x + x2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + -0.625x + 1.375 + x2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + -0.625x + x2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + -0.625x + x2 = 0 + 1.375 -0.625x + x2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 -0.625x + x2 = 1.375 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 1.375 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 1.375 + 0.09765625 Combine like terms: 1.375 + 0.09765625 = 1.47265625 0.09765625 + -0.625x + x2 = 1.47265625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 1.47265625 Calculate the square root of the right side: 1.21353049 Break this problem into two subproblems by setting (x + -0.3125) equal to 1.21353049 and -1.21353049.Subproblem 1
x + -0.3125 = 1.21353049 Simplifying x + -0.3125 = 1.21353049 Reorder the terms: -0.3125 + x = 1.21353049 Solving -0.3125 + x = 1.21353049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 1.21353049 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 1.21353049 + 0.3125 x = 1.21353049 + 0.3125 Combine like terms: 1.21353049 + 0.3125 = 1.52603049 x = 1.52603049 Simplifying x = 1.52603049Subproblem 2
x + -0.3125 = -1.21353049 Simplifying x + -0.3125 = -1.21353049 Reorder the terms: -0.3125 + x = -1.21353049 Solving -0.3125 + x = -1.21353049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -1.21353049 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -1.21353049 + 0.3125 x = -1.21353049 + 0.3125 Combine like terms: -1.21353049 + 0.3125 = -0.90103049 x = -0.90103049 Simplifying x = -0.90103049Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.52603049, -0.90103049}
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