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Simplifying x(0.3 + x) = (0.2 + -1x) (0.3 * x + x * x) = (0.2 + -1x) (0.3x + x2) = (0.2 + -1x) Remove parenthesis around (0.2 + -1x) 0.3x + x2 = 0.2 + -1x Solving 0.3x + x2 = 0.2 + -1x Solving for variable 'x'. Reorder the terms: -0.2 + 0.3x + x + x2 = 0.2 + -1x + -0.2 + x Combine like terms: 0.3x + x = 1.3x -0.2 + 1.3x + x2 = 0.2 + -1x + -0.2 + x Reorder the terms: -0.2 + 1.3x + x2 = 0.2 + -0.2 + -1x + x Combine like terms: 0.2 + -0.2 = 0.0 -0.2 + 1.3x + x2 = 0.0 + -1x + x -0.2 + 1.3x + x2 = -1x + x Combine like terms: -1x + x = 0 -0.2 + 1.3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 1.3x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 1.3x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 1.3x + x2 = 0 + 0.2 1.3x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 1.3x + x2 = 0.2 The x term is 1.3x. Take half its coefficient (0.65). Square it (0.4225) and add it to both sides. Add '0.4225' to each side of the equation. 1.3x + 0.4225 + x2 = 0.2 + 0.4225 Reorder the terms: 0.4225 + 1.3x + x2 = 0.2 + 0.4225 Combine like terms: 0.2 + 0.4225 = 0.6225 0.4225 + 1.3x + x2 = 0.6225 Factor a perfect square on the left side: (x + 0.65)(x + 0.65) = 0.6225 Calculate the square root of the right side: 0.788986692 Break this problem into two subproblems by setting (x + 0.65) equal to 0.788986692 and -0.788986692.Subproblem 1
x + 0.65 = 0.788986692 Simplifying x + 0.65 = 0.788986692 Reorder the terms: 0.65 + x = 0.788986692 Solving 0.65 + x = 0.788986692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + x = 0.788986692 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + x = 0.788986692 + -0.65 x = 0.788986692 + -0.65 Combine like terms: 0.788986692 + -0.65 = 0.138986692 x = 0.138986692 Simplifying x = 0.138986692Subproblem 2
x + 0.65 = -0.788986692 Simplifying x + 0.65 = -0.788986692 Reorder the terms: 0.65 + x = -0.788986692 Solving 0.65 + x = -0.788986692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65' to each side of the equation. 0.65 + -0.65 + x = -0.788986692 + -0.65 Combine like terms: 0.65 + -0.65 = 0.00 0.00 + x = -0.788986692 + -0.65 x = -0.788986692 + -0.65 Combine like terms: -0.788986692 + -0.65 = -1.438986692 x = -1.438986692 Simplifying x = -1.438986692Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.138986692, -1.438986692}
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