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Simplifying 34x2 + -4x + -89 = 0 Reorder the terms: -89 + -4x + 34x2 = 0 Solving -89 + -4x + 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 + -0.1176470588x + x2 = 0 Move the constant term to the right: Add '2.617647059' to each side of the equation. -2.617647059 + -0.1176470588x + 2.617647059 + x2 = 0 + 2.617647059 Reorder the terms: -2.617647059 + 2.617647059 + -0.1176470588x + x2 = 0 + 2.617647059 Combine like terms: -2.617647059 + 2.617647059 = 0.000000000 0.000000000 + -0.1176470588x + x2 = 0 + 2.617647059 -0.1176470588x + x2 = 0 + 2.617647059 Combine like terms: 0 + 2.617647059 = 2.617647059 -0.1176470588x + x2 = 2.617647059 The x term is -0.1176470588x. Take half its coefficient (-0.0588235294). Square it (0.003460207611) and add it to both sides. Add '0.003460207611' to each side of the equation. -0.1176470588x + 0.003460207611 + x2 = 2.617647059 + 0.003460207611 Reorder the terms: 0.003460207611 + -0.1176470588x + x2 = 2.617647059 + 0.003460207611 Combine like terms: 2.617647059 + 0.003460207611 = 2.621107266611 0.003460207611 + -0.1176470588x + x2 = 2.621107266611 Factor a perfect square on the left side: (x + -0.0588235294)(x + -0.0588235294) = 2.621107266611 Calculate the square root of the right side: 1.618983405 Break this problem into two subproblems by setting (x + -0.0588235294) equal to 1.618983405 and -1.618983405.Subproblem 1
x + -0.0588235294 = 1.618983405 Simplifying x + -0.0588235294 = 1.618983405 Reorder the terms: -0.0588235294 + x = 1.618983405 Solving -0.0588235294 + x = 1.618983405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0588235294' to each side of the equation. -0.0588235294 + 0.0588235294 + x = 1.618983405 + 0.0588235294 Combine like terms: -0.0588235294 + 0.0588235294 = 0.0000000000 0.0000000000 + x = 1.618983405 + 0.0588235294 x = 1.618983405 + 0.0588235294 Combine like terms: 1.618983405 + 0.0588235294 = 1.6778069344 x = 1.6778069344 Simplifying x = 1.6778069344Subproblem 2
x + -0.0588235294 = -1.618983405 Simplifying x + -0.0588235294 = -1.618983405 Reorder the terms: -0.0588235294 + x = -1.618983405 Solving -0.0588235294 + x = -1.618983405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0588235294' to each side of the equation. -0.0588235294 + 0.0588235294 + x = -1.618983405 + 0.0588235294 Combine like terms: -0.0588235294 + 0.0588235294 = 0.0000000000 0.0000000000 + x = -1.618983405 + 0.0588235294 x = -1.618983405 + 0.0588235294 Combine like terms: -1.618983405 + 0.0588235294 = -1.5601598756 x = -1.5601598756 Simplifying x = -1.5601598756Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6778069344, -1.5601598756}
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