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Simplifying 6x + 3x2 = 1.6 Solving 6x + 3x2 = 1.6 Solving for variable 'x'. Reorder the terms: -1.6 + 6x + 3x2 = 1.6 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 -1.6 + 6x + 3x2 = 0.0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.5333333333 + 2x + x2 = 0.0 Move the constant term to the right: Add '0.5333333333' to each side of the equation. -0.5333333333 + 2x + 0.5333333333 + x2 = 0.0 + 0.5333333333 Reorder the terms: -0.5333333333 + 0.5333333333 + 2x + x2 = 0.0 + 0.5333333333 Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000 0.0000000000 + 2x + x2 = 0.0 + 0.5333333333 2x + x2 = 0.0 + 0.5333333333 Combine like terms: 0.0 + 0.5333333333 = 0.5333333333 2x + x2 = 0.5333333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.5333333333 + 1 Reorder the terms: 1 + 2x + x2 = 0.5333333333 + 1 Combine like terms: 0.5333333333 + 1 = 1.5333333333 1 + 2x + x2 = 1.5333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.5333333333 Calculate the square root of the right side: 1.238278375 Break this problem into two subproblems by setting (x + 1) equal to 1.238278375 and -1.238278375.Subproblem 1
x + 1 = 1.238278375 Simplifying x + 1 = 1.238278375 Reorder the terms: 1 + x = 1.238278375 Solving 1 + x = 1.238278375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.238278375 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.238278375 + -1 x = 1.238278375 + -1 Combine like terms: 1.238278375 + -1 = 0.238278375 x = 0.238278375 Simplifying x = 0.238278375Subproblem 2
x + 1 = -1.238278375 Simplifying x + 1 = -1.238278375 Reorder the terms: 1 + x = -1.238278375 Solving 1 + x = -1.238278375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.238278375 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.238278375 + -1 x = -1.238278375 + -1 Combine like terms: -1.238278375 + -1 = -2.238278375 x = -2.238278375 Simplifying x = -2.238278375Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.238278375, -2.238278375}
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