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Simplifying 1.7x2 + x + -1.6 = 0 Reorder the terms: -1.6 + x + 1.7x2 = 0 Solving -1.6 + x + 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'. -0.9411764706 + 0.5882352941x + x2 = 0 Move the constant term to the right: Add '0.9411764706' to each side of the equation. -0.9411764706 + 0.5882352941x + 0.9411764706 + x2 = 0 + 0.9411764706 Reorder the terms: -0.9411764706 + 0.9411764706 + 0.5882352941x + x2 = 0 + 0.9411764706 Combine like terms: -0.9411764706 + 0.9411764706 = 0.0000000000 0.0000000000 + 0.5882352941x + x2 = 0 + 0.9411764706 0.5882352941x + x2 = 0 + 0.9411764706 Combine like terms: 0 + 0.9411764706 = 0.9411764706 0.5882352941x + x2 = 0.9411764706 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5882352941x + 0.25 + x2 = 0.9411764706 + 0.25 Reorder the terms: 0.25 + 0.5882352941x + x2 = 0.9411764706 + 0.25 Combine like terms: 0.9411764706 + 0.25 = 1.1911764706 0.25 + 0.5882352941x + x2 = 1.1911764706 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.1911764706 Calculate the square root of the right side: 1.091410313 Break this problem into two subproblems by setting (x + 0.5) equal to 1.091410313 and -1.091410313.Subproblem 1
x + 0.5 = 1.091410313 Simplifying x + 0.5 = 1.091410313 Reorder the terms: 0.5 + x = 1.091410313 Solving 0.5 + x = 1.091410313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.091410313 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.091410313 + -0.5 x = 1.091410313 + -0.5 Combine like terms: 1.091410313 + -0.5 = 0.591410313 x = 0.591410313 Simplifying x = 0.591410313Subproblem 2
x + 0.5 = -1.091410313 Simplifying x + 0.5 = -1.091410313 Reorder the terms: 0.5 + x = -1.091410313 Solving 0.5 + x = -1.091410313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.091410313 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.091410313 + -0.5 x = -1.091410313 + -0.5 Combine like terms: -1.091410313 + -0.5 = -1.591410313 x = -1.591410313 Simplifying x = -1.591410313Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.591410313, -1.591410313}
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