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Simplifying (7x2 + -3x + -55) + (9x2 + 6x) = 0 Reorder the terms: (-55 + -3x + 7x2) + (9x2 + 6x) = 0 Remove parenthesis around (-55 + -3x + 7x2) -55 + -3x + 7x2 + (9x2 + 6x) = 0 Reorder the terms: -55 + -3x + 7x2 + (6x + 9x2) = 0 Remove parenthesis around (6x + 9x2) -55 + -3x + 7x2 + 6x + 9x2 = 0 Reorder the terms: -55 + -3x + 6x + 7x2 + 9x2 = 0 Combine like terms: -3x + 6x = 3x -55 + 3x + 7x2 + 9x2 = 0 Combine like terms: 7x2 + 9x2 = 16x2 -55 + 3x + 16x2 = 0 Solving -55 + 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'. -3.4375 + 0.1875x + x2 = 0 Move the constant term to the right: Add '3.4375' to each side of the equation. -3.4375 + 0.1875x + 3.4375 + x2 = 0 + 3.4375 Reorder the terms: -3.4375 + 3.4375 + 0.1875x + x2 = 0 + 3.4375 Combine like terms: -3.4375 + 3.4375 = 0.0000 0.0000 + 0.1875x + x2 = 0 + 3.4375 0.1875x + x2 = 0 + 3.4375 Combine like terms: 0 + 3.4375 = 3.4375 0.1875x + x2 = 3.4375 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 = 3.4375 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = 3.4375 + 0.0087890625 Combine like terms: 3.4375 + 0.0087890625 = 3.4462890625 0.0087890625 + 0.1875x + x2 = 3.4462890625 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = 3.4462890625 Calculate the square root of the right side: 1.856418343 Break this problem into two subproblems by setting (x + 0.09375) equal to 1.856418343 and -1.856418343.Subproblem 1
x + 0.09375 = 1.856418343 Simplifying x + 0.09375 = 1.856418343 Reorder the terms: 0.09375 + x = 1.856418343 Solving 0.09375 + x = 1.856418343 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 = 1.856418343 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 1.856418343 + -0.09375 x = 1.856418343 + -0.09375 Combine like terms: 1.856418343 + -0.09375 = 1.762668343 x = 1.762668343 Simplifying x = 1.762668343Subproblem 2
x + 0.09375 = -1.856418343 Simplifying x + 0.09375 = -1.856418343 Reorder the terms: 0.09375 + x = -1.856418343 Solving 0.09375 + x = -1.856418343 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 = -1.856418343 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -1.856418343 + -0.09375 x = -1.856418343 + -0.09375 Combine like terms: -1.856418343 + -0.09375 = -1.950168343 x = -1.950168343 Simplifying x = -1.950168343Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.762668343, -1.950168343}
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