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Simplifying (11x2 + -2x + 15) + (5x2 + 5x + -46) = 0 Reorder the terms: (15 + -2x + 11x2) + (5x2 + 5x + -46) = 0 Remove parenthesis around (15 + -2x + 11x2) 15 + -2x + 11x2 + (5x2 + 5x + -46) = 0 Reorder the terms: 15 + -2x + 11x2 + (-46 + 5x + 5x2) = 0 Remove parenthesis around (-46 + 5x + 5x2) 15 + -2x + 11x2 + -46 + 5x + 5x2 = 0 Reorder the terms: 15 + -46 + -2x + 5x + 11x2 + 5x2 = 0 Combine like terms: 15 + -46 = -31 -31 + -2x + 5x + 11x2 + 5x2 = 0 Combine like terms: -2x + 5x = 3x -31 + 3x + 11x2 + 5x2 = 0 Combine like terms: 11x2 + 5x2 = 16x2 -31 + 3x + 16x2 = 0 Solving -31 + 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'. -1.9375 + 0.1875x + x2 = 0 Move the constant term to the right: Add '1.9375' to each side of the equation. -1.9375 + 0.1875x + 1.9375 + x2 = 0 + 1.9375 Reorder the terms: -1.9375 + 1.9375 + 0.1875x + x2 = 0 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + 0.1875x + x2 = 0 + 1.9375 0.1875x + x2 = 0 + 1.9375 Combine like terms: 0 + 1.9375 = 1.9375 0.1875x + x2 = 1.9375 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 = 1.9375 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = 1.9375 + 0.0087890625 Combine like terms: 1.9375 + 0.0087890625 = 1.9462890625 0.0087890625 + 0.1875x + x2 = 1.9462890625 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = 1.9462890625 Calculate the square root of the right side: 1.395094643 Break this problem into two subproblems by setting (x + 0.09375) equal to 1.395094643 and -1.395094643.Subproblem 1
x + 0.09375 = 1.395094643 Simplifying x + 0.09375 = 1.395094643 Reorder the terms: 0.09375 + x = 1.395094643 Solving 0.09375 + x = 1.395094643 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 = 1.395094643 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 1.395094643 + -0.09375 x = 1.395094643 + -0.09375 Combine like terms: 1.395094643 + -0.09375 = 1.301344643 x = 1.301344643 Simplifying x = 1.301344643Subproblem 2
x + 0.09375 = -1.395094643 Simplifying x + 0.09375 = -1.395094643 Reorder the terms: 0.09375 + x = -1.395094643 Solving 0.09375 + x = -1.395094643 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 = -1.395094643 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -1.395094643 + -0.09375 x = -1.395094643 + -0.09375 Combine like terms: -1.395094643 + -0.09375 = -1.488844643 x = -1.488844643 Simplifying x = -1.488844643Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.301344643, -1.488844643}
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