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Simplifying 11 + 3x + -4x * 4x = 0 Reorder the terms for easier multiplication: 11 + 3x + -4 * 4x * x = 0 Multiply -4 * 4 11 + 3x + -16x * x = 0 Multiply x * x 11 + 3x + -16x2 = 0 Solving 11 + 3x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.6875 + -0.1875x + x2 = 0 Move the constant term to the right: Add '0.6875' to each side of the equation. -0.6875 + -0.1875x + 0.6875 + x2 = 0 + 0.6875 Reorder the terms: -0.6875 + 0.6875 + -0.1875x + x2 = 0 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + -0.1875x + x2 = 0 + 0.6875 -0.1875x + x2 = 0 + 0.6875 Combine like terms: 0 + 0.6875 = 0.6875 -0.1875x + x2 = 0.6875 The x term is -0.1875x. Take half its coefficient (-0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. -0.1875x + 0.0087890625 + x2 = 0.6875 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875x + x2 = 0.6875 + 0.0087890625 Combine like terms: 0.6875 + 0.0087890625 = 0.6962890625 0.0087890625 + -0.1875x + x2 = 0.6962890625 Factor a perfect square on the left side: (x + -0.09375)(x + -0.09375) = 0.6962890625 Calculate the square root of the right side: 0.83443937 Break this problem into two subproblems by setting (x + -0.09375) equal to 0.83443937 and -0.83443937.Subproblem 1
x + -0.09375 = 0.83443937 Simplifying x + -0.09375 = 0.83443937 Reorder the terms: -0.09375 + x = 0.83443937 Solving -0.09375 + x = 0.83443937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = 0.83443937 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = 0.83443937 + 0.09375 x = 0.83443937 + 0.09375 Combine like terms: 0.83443937 + 0.09375 = 0.92818937 x = 0.92818937 Simplifying x = 0.92818937Subproblem 2
x + -0.09375 = -0.83443937 Simplifying x + -0.09375 = -0.83443937 Reorder the terms: -0.09375 + x = -0.83443937 Solving -0.09375 + x = -0.83443937 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09375' to each side of the equation. -0.09375 + 0.09375 + x = -0.83443937 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = -0.83443937 + 0.09375 x = -0.83443937 + 0.09375 Combine like terms: -0.83443937 + 0.09375 = -0.74068937 x = -0.74068937 Simplifying x = -0.74068937Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.92818937, -0.74068937}
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