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Simplifying 16x2 + 3x + -11 = 0 Reorder the terms: -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 = 0.74068937 x = 0.74068937 Simplifying x = 0.74068937Subproblem 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 = -0.92818937 x = -0.92818937 Simplifying x = -0.92818937Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.74068937, -0.92818937}
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