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Simplifying 1.7x2 + -2.9x + 1 = 0 Reorder the terms: 1 + -2.9x + 1.7x2 = 0 Solving 1 + -2.9x + 1.7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.7 the coefficient of the squared term: Divide each side by '1.7'. 0.5882352941 + -1.705882353x + x2 = 0 Move the constant term to the right: Add '-0.5882352941' to each side of the equation. 0.5882352941 + -1.705882353x + -0.5882352941 + x2 = 0 + -0.5882352941 Reorder the terms: 0.5882352941 + -0.5882352941 + -1.705882353x + x2 = 0 + -0.5882352941 Combine like terms: 0.5882352941 + -0.5882352941 = 0.0000000000 0.0000000000 + -1.705882353x + x2 = 0 + -0.5882352941 -1.705882353x + x2 = 0 + -0.5882352941 Combine like terms: 0 + -0.5882352941 = -0.5882352941 -1.705882353x + x2 = -0.5882352941 The x term is -1.705882353x. Take half its coefficient (-0.8529411765). Square it (0.7275086506) and add it to both sides. Add '0.7275086506' to each side of the equation. -1.705882353x + 0.7275086506 + x2 = -0.5882352941 + 0.7275086506 Reorder the terms: 0.7275086506 + -1.705882353x + x2 = -0.5882352941 + 0.7275086506 Combine like terms: -0.5882352941 + 0.7275086506 = 0.1392733565 0.7275086506 + -1.705882353x + x2 = 0.1392733565 Factor a perfect square on the left side: (x + -0.8529411765)(x + -0.8529411765) = 0.1392733565 Calculate the square root of the right side: 0.373193457 Break this problem into two subproblems by setting (x + -0.8529411765) equal to 0.373193457 and -0.373193457.Subproblem 1
x + -0.8529411765 = 0.373193457 Simplifying x + -0.8529411765 = 0.373193457 Reorder the terms: -0.8529411765 + x = 0.373193457 Solving -0.8529411765 + x = 0.373193457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8529411765' to each side of the equation. -0.8529411765 + 0.8529411765 + x = 0.373193457 + 0.8529411765 Combine like terms: -0.8529411765 + 0.8529411765 = 0.0000000000 0.0000000000 + x = 0.373193457 + 0.8529411765 x = 0.373193457 + 0.8529411765 Combine like terms: 0.373193457 + 0.8529411765 = 1.2261346335 x = 1.2261346335 Simplifying x = 1.2261346335Subproblem 2
x + -0.8529411765 = -0.373193457 Simplifying x + -0.8529411765 = -0.373193457 Reorder the terms: -0.8529411765 + x = -0.373193457 Solving -0.8529411765 + x = -0.373193457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8529411765' to each side of the equation. -0.8529411765 + 0.8529411765 + x = -0.373193457 + 0.8529411765 Combine like terms: -0.8529411765 + 0.8529411765 = 0.0000000000 0.0000000000 + x = -0.373193457 + 0.8529411765 x = -0.373193457 + 0.8529411765 Combine like terms: -0.373193457 + 0.8529411765 = 0.4797477195 x = 0.4797477195 Simplifying x = 0.4797477195Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2261346335, 0.4797477195}
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