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Simplifying x = -16x2 + 4x + 26 Reorder the terms: x = 26 + 4x + -16x2 Solving x = 26 + 4x + -16x2 Solving for variable 'x'. Reorder the terms: -26 + x + -4x + 16x2 = 26 + 4x + -16x2 + -26 + -4x + 16x2 Combine like terms: x + -4x = -3x -26 + -3x + 16x2 = 26 + 4x + -16x2 + -26 + -4x + 16x2 Reorder the terms: -26 + -3x + 16x2 = 26 + -26 + 4x + -4x + -16x2 + 16x2 Combine like terms: 26 + -26 = 0 -26 + -3x + 16x2 = 0 + 4x + -4x + -16x2 + 16x2 -26 + -3x + 16x2 = 4x + -4x + -16x2 + 16x2 Combine like terms: 4x + -4x = 0 -26 + -3x + 16x2 = 0 + -16x2 + 16x2 -26 + -3x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -26 + -3x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -1.625 + -0.1875x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + -0.1875x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + -0.1875x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + -0.1875x + x2 = 0 + 1.625 -0.1875x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 -0.1875x + x2 = 1.625 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 = 1.625 + 0.0087890625 Reorder the terms: 0.0087890625 + -0.1875x + x2 = 1.625 + 0.0087890625 Combine like terms: 1.625 + 0.0087890625 = 1.6337890625 0.0087890625 + -0.1875x + x2 = 1.6337890625 Factor a perfect square on the left side: (x + -0.09375)(x + -0.09375) = 1.6337890625 Calculate the square root of the right side: 1.278197584 Break this problem into two subproblems by setting (x + -0.09375) equal to 1.278197584 and -1.278197584.Subproblem 1
x + -0.09375 = 1.278197584 Simplifying x + -0.09375 = 1.278197584 Reorder the terms: -0.09375 + x = 1.278197584 Solving -0.09375 + x = 1.278197584 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 = 1.278197584 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = 1.278197584 + 0.09375 x = 1.278197584 + 0.09375 Combine like terms: 1.278197584 + 0.09375 = 1.371947584 x = 1.371947584 Simplifying x = 1.371947584Subproblem 2
x + -0.09375 = -1.278197584 Simplifying x + -0.09375 = -1.278197584 Reorder the terms: -0.09375 + x = -1.278197584 Solving -0.09375 + x = -1.278197584 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 = -1.278197584 + 0.09375 Combine like terms: -0.09375 + 0.09375 = 0.00000 0.00000 + x = -1.278197584 + 0.09375 x = -1.278197584 + 0.09375 Combine like terms: -1.278197584 + 0.09375 = -1.184447584 x = -1.184447584 Simplifying x = -1.184447584Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.371947584, -1.184447584}
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