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Simplifying 4x(4x + -11) = 11 Reorder the terms: 4x(-11 + 4x) = 11 (-11 * 4x + 4x * 4x) = 11 (-44x + 16x2) = 11 Solving -44x + 16x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -44x + 16x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -44x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.6875 + -2.75x + x2 = 0 Move the constant term to the right: Add '0.6875' to each side of the equation. -0.6875 + -2.75x + 0.6875 + x2 = 0 + 0.6875 Reorder the terms: -0.6875 + 0.6875 + -2.75x + x2 = 0 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + -2.75x + x2 = 0 + 0.6875 -2.75x + x2 = 0 + 0.6875 Combine like terms: 0 + 0.6875 = 0.6875 -2.75x + x2 = 0.6875 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = 0.6875 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = 0.6875 + 1.890625 Combine like terms: 0.6875 + 1.890625 = 2.578125 1.890625 + -2.75x + x2 = 2.578125 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = 2.578125 Calculate the square root of the right side: 1.605654072 Break this problem into two subproblems by setting (x + -1.375) equal to 1.605654072 and -1.605654072.Subproblem 1
x + -1.375 = 1.605654072 Simplifying x + -1.375 = 1.605654072 Reorder the terms: -1.375 + x = 1.605654072 Solving -1.375 + x = 1.605654072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = 1.605654072 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = 1.605654072 + 1.375 x = 1.605654072 + 1.375 Combine like terms: 1.605654072 + 1.375 = 2.980654072 x = 2.980654072 Simplifying x = 2.980654072Subproblem 2
x + -1.375 = -1.605654072 Simplifying x + -1.375 = -1.605654072 Reorder the terms: -1.375 + x = -1.605654072 Solving -1.375 + x = -1.605654072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.375' to each side of the equation. -1.375 + 1.375 + x = -1.605654072 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + x = -1.605654072 + 1.375 x = -1.605654072 + 1.375 Combine like terms: -1.605654072 + 1.375 = -0.230654072 x = -0.230654072 Simplifying x = -0.230654072Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.980654072, -0.230654072}
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