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Simplifying 8x2 = 11x + -2 Reorder the terms: 8x2 = -2 + 11x Solving 8x2 = -2 + 11x Solving for variable 'x'. Reorder the terms: 2 + -11x + 8x2 = -2 + 11x + 2 + -11x Reorder the terms: 2 + -11x + 8x2 = -2 + 2 + 11x + -11x Combine like terms: -2 + 2 = 0 2 + -11x + 8x2 = 0 + 11x + -11x 2 + -11x + 8x2 = 11x + -11x Combine like terms: 11x + -11x = 0 2 + -11x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.25 + -1.375x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -1.375x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -1.375x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -1.375x + x2 = 0 + -0.25 -1.375x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -1.375x + x2 = -0.25 The x term is -1.375x. Take half its coefficient (-0.6875). Square it (0.47265625) and add it to both sides. Add '0.47265625' to each side of the equation. -1.375x + 0.47265625 + x2 = -0.25 + 0.47265625 Reorder the terms: 0.47265625 + -1.375x + x2 = -0.25 + 0.47265625 Combine like terms: -0.25 + 0.47265625 = 0.22265625 0.47265625 + -1.375x + x2 = 0.22265625 Factor a perfect square on the left side: (x + -0.6875)(x + -0.6875) = 0.22265625 Calculate the square root of the right side: 0.471864652 Break this problem into two subproblems by setting (x + -0.6875) equal to 0.471864652 and -0.471864652.Subproblem 1
x + -0.6875 = 0.471864652 Simplifying x + -0.6875 = 0.471864652 Reorder the terms: -0.6875 + x = 0.471864652 Solving -0.6875 + x = 0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = 0.471864652 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = 0.471864652 + 0.6875 x = 0.471864652 + 0.6875 Combine like terms: 0.471864652 + 0.6875 = 1.159364652 x = 1.159364652 Simplifying x = 1.159364652Subproblem 2
x + -0.6875 = -0.471864652 Simplifying x + -0.6875 = -0.471864652 Reorder the terms: -0.6875 + x = -0.471864652 Solving -0.6875 + x = -0.471864652 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = -0.471864652 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = -0.471864652 + 0.6875 x = -0.471864652 + 0.6875 Combine like terms: -0.471864652 + 0.6875 = 0.215635348 x = 0.215635348 Simplifying x = 0.215635348Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.159364652, 0.215635348}
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