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Simplifying (7x2 + -5x + 14) + (9x2 + 8x + -48) = 0 Reorder the terms: (14 + -5x + 7x2) + (9x2 + 8x + -48) = 0 Remove parenthesis around (14 + -5x + 7x2) 14 + -5x + 7x2 + (9x2 + 8x + -48) = 0 Reorder the terms: 14 + -5x + 7x2 + (-48 + 8x + 9x2) = 0 Remove parenthesis around (-48 + 8x + 9x2) 14 + -5x + 7x2 + -48 + 8x + 9x2 = 0 Reorder the terms: 14 + -48 + -5x + 8x + 7x2 + 9x2 = 0 Combine like terms: 14 + -48 = -34 -34 + -5x + 8x + 7x2 + 9x2 = 0 Combine like terms: -5x + 8x = 3x -34 + 3x + 7x2 + 9x2 = 0 Combine like terms: 7x2 + 9x2 = 16x2 -34 + 3x + 16x2 = 0 Solving -34 + 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'. -2.125 + 0.1875x + x2 = 0 Move the constant term to the right: Add '2.125' to each side of the equation. -2.125 + 0.1875x + 2.125 + x2 = 0 + 2.125 Reorder the terms: -2.125 + 2.125 + 0.1875x + x2 = 0 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + 0.1875x + x2 = 0 + 2.125 0.1875x + x2 = 0 + 2.125 Combine like terms: 0 + 2.125 = 2.125 0.1875x + x2 = 2.125 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 = 2.125 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = 2.125 + 0.0087890625 Combine like terms: 2.125 + 0.0087890625 = 2.1337890625 0.0087890625 + 0.1875x + x2 = 2.1337890625 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = 2.1337890625 Calculate the square root of the right side: 1.460749487 Break this problem into two subproblems by setting (x + 0.09375) equal to 1.460749487 and -1.460749487.Subproblem 1
x + 0.09375 = 1.460749487 Simplifying x + 0.09375 = 1.460749487 Reorder the terms: 0.09375 + x = 1.460749487 Solving 0.09375 + x = 1.460749487 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 = 1.460749487 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 1.460749487 + -0.09375 x = 1.460749487 + -0.09375 Combine like terms: 1.460749487 + -0.09375 = 1.366999487 x = 1.366999487 Simplifying x = 1.366999487Subproblem 2
x + 0.09375 = -1.460749487 Simplifying x + 0.09375 = -1.460749487 Reorder the terms: 0.09375 + x = -1.460749487 Solving 0.09375 + x = -1.460749487 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 = -1.460749487 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -1.460749487 + -0.09375 x = -1.460749487 + -0.09375 Combine like terms: -1.460749487 + -0.09375 = -1.554499487 x = -1.554499487 Simplifying x = -1.554499487Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.366999487, -1.554499487}
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