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Simplifying 0.23 = (4 + -1x) * x Reorder the terms for easier multiplication: 0.23 = x(4 + -1x) 0.23 = (4 * x + -1x * x) 0.23 = (4x + -1x2) Solving 0.23 = 4x + -1x2 Solving for variable 'x'. Reorder the terms: 0.23 + -4x + x2 = 4x + -4x + -1x2 + x2 Combine like terms: 4x + -4x = 0 0.23 + -4x + x2 = 0 + -1x2 + x2 0.23 + -4x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 0.23 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-0.23' to each side of the equation. 0.23 + -4x + -0.23 + x2 = 0 + -0.23 Reorder the terms: 0.23 + -0.23 + -4x + x2 = 0 + -0.23 Combine like terms: 0.23 + -0.23 = 0.00 0.00 + -4x + x2 = 0 + -0.23 -4x + x2 = 0 + -0.23 Combine like terms: 0 + -0.23 = -0.23 -4x + x2 = -0.23 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -0.23 + 4 Reorder the terms: 4 + -4x + x2 = -0.23 + 4 Combine like terms: -0.23 + 4 = 3.77 4 + -4x + x2 = 3.77 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.77 Calculate the square root of the right side: 1.941648784 Break this problem into two subproblems by setting (x + -2) equal to 1.941648784 and -1.941648784.Subproblem 1
x + -2 = 1.941648784 Simplifying x + -2 = 1.941648784 Reorder the terms: -2 + x = 1.941648784 Solving -2 + x = 1.941648784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.941648784 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.941648784 + 2 x = 1.941648784 + 2 Combine like terms: 1.941648784 + 2 = 3.941648784 x = 3.941648784 Simplifying x = 3.941648784Subproblem 2
x + -2 = -1.941648784 Simplifying x + -2 = -1.941648784 Reorder the terms: -2 + x = -1.941648784 Solving -2 + x = -1.941648784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.941648784 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.941648784 + 2 x = -1.941648784 + 2 Combine like terms: -1.941648784 + 2 = 0.058351216 x = 0.058351216 Simplifying x = 0.058351216Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.941648784, 0.058351216}
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