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Simplifying x(x + 0.19) = 0.084 Reorder the terms: x(0.19 + x) = 0.084 (0.19 * x + x * x) = 0.084 (0.19x + x2) = 0.084 Solving 0.19x + x2 = 0.084 Solving for variable 'x'. Reorder the terms: -0.084 + 0.19x + x2 = 0.084 + -0.084 Combine like terms: 0.084 + -0.084 = 0.000 -0.084 + 0.19x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '0.084' to each side of the equation. -0.084 + 0.19x + 0.084 + x2 = 0.000 + 0.084 Reorder the terms: -0.084 + 0.084 + 0.19x + x2 = 0.000 + 0.084 Combine like terms: -0.084 + 0.084 = 0.000 0.000 + 0.19x + x2 = 0.000 + 0.084 0.19x + x2 = 0.000 + 0.084 Combine like terms: 0.000 + 0.084 = 0.084 0.19x + x2 = 0.084 The x term is 0.19x. Take half its coefficient (0.095). Square it (0.009025) and add it to both sides. Add '0.009025' to each side of the equation. 0.19x + 0.009025 + x2 = 0.084 + 0.009025 Reorder the terms: 0.009025 + 0.19x + x2 = 0.084 + 0.009025 Combine like terms: 0.084 + 0.009025 = 0.093025 0.009025 + 0.19x + x2 = 0.093025 Factor a perfect square on the left side: (x + 0.095)(x + 0.095) = 0.093025 Calculate the square root of the right side: 0.305 Break this problem into two subproblems by setting (x + 0.095) equal to 0.305 and -0.305.Subproblem 1
x + 0.095 = 0.305 Simplifying x + 0.095 = 0.305 Reorder the terms: 0.095 + x = 0.305 Solving 0.095 + x = 0.305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.095' to each side of the equation. 0.095 + -0.095 + x = 0.305 + -0.095 Combine like terms: 0.095 + -0.095 = 0.000 0.000 + x = 0.305 + -0.095 x = 0.305 + -0.095 Combine like terms: 0.305 + -0.095 = 0.21 x = 0.21 Simplifying x = 0.21Subproblem 2
x + 0.095 = -0.305 Simplifying x + 0.095 = -0.305 Reorder the terms: 0.095 + x = -0.305 Solving 0.095 + x = -0.305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.095' to each side of the equation. 0.095 + -0.095 + x = -0.305 + -0.095 Combine like terms: 0.095 + -0.095 = 0.000 0.000 + x = -0.305 + -0.095 x = -0.305 + -0.095 Combine like terms: -0.305 + -0.095 = -0.4 x = -0.4 Simplifying x = -0.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.21, -0.4}
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