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Simplifying 34x2 + 56x + -89 = 0 Reorder the terms: -89 + 56x + 34x2 = 0 Solving -89 + 56x + 34x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. -2.617647059 + 1.647058824x + x2 = 0 Move the constant term to the right: Add '2.617647059' to each side of the equation. -2.617647059 + 1.647058824x + 2.617647059 + x2 = 0 + 2.617647059 Reorder the terms: -2.617647059 + 2.617647059 + 1.647058824x + x2 = 0 + 2.617647059 Combine like terms: -2.617647059 + 2.617647059 = 0.000000000 0.000000000 + 1.647058824x + x2 = 0 + 2.617647059 1.647058824x + x2 = 0 + 2.617647059 Combine like terms: 0 + 2.617647059 = 2.617647059 1.647058824x + x2 = 2.617647059 The x term is 1.647058824x. Take half its coefficient (0.823529412). Square it (0.6782006924) and add it to both sides. Add '0.6782006924' to each side of the equation. 1.647058824x + 0.6782006924 + x2 = 2.617647059 + 0.6782006924 Reorder the terms: 0.6782006924 + 1.647058824x + x2 = 2.617647059 + 0.6782006924 Combine like terms: 2.617647059 + 0.6782006924 = 3.2958477514 0.6782006924 + 1.647058824x + x2 = 3.2958477514 Factor a perfect square on the left side: (x + 0.823529412)(x + 0.823529412) = 3.2958477514 Calculate the square root of the right side: 1.815446984 Break this problem into two subproblems by setting (x + 0.823529412) equal to 1.815446984 and -1.815446984.Subproblem 1
x + 0.823529412 = 1.815446984 Simplifying x + 0.823529412 = 1.815446984 Reorder the terms: 0.823529412 + x = 1.815446984 Solving 0.823529412 + x = 1.815446984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.823529412' to each side of the equation. 0.823529412 + -0.823529412 + x = 1.815446984 + -0.823529412 Combine like terms: 0.823529412 + -0.823529412 = 0.000000000 0.000000000 + x = 1.815446984 + -0.823529412 x = 1.815446984 + -0.823529412 Combine like terms: 1.815446984 + -0.823529412 = 0.991917572 x = 0.991917572 Simplifying x = 0.991917572Subproblem 2
x + 0.823529412 = -1.815446984 Simplifying x + 0.823529412 = -1.815446984 Reorder the terms: 0.823529412 + x = -1.815446984 Solving 0.823529412 + x = -1.815446984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.823529412' to each side of the equation. 0.823529412 + -0.823529412 + x = -1.815446984 + -0.823529412 Combine like terms: 0.823529412 + -0.823529412 = 0.000000000 0.000000000 + x = -1.815446984 + -0.823529412 x = -1.815446984 + -0.823529412 Combine like terms: -1.815446984 + -0.823529412 = -2.638976396 x = -2.638976396 Simplifying x = -2.638976396Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.991917572, -2.638976396}
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