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Simplifying x2 + 0.19x + -0.4(0.19) = 0 Multiply -0.4 * 0.19 x2 + 0.19x + -0.076 = 0 Reorder the terms: -0.076 + 0.19x + x2 = 0 Solving -0.076 + 0.19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.076' to each side of the equation. -0.076 + 0.19x + 0.076 + x2 = 0 + 0.076 Reorder the terms: -0.076 + 0.076 + 0.19x + x2 = 0 + 0.076 Combine like terms: -0.076 + 0.076 = 0.000 0.000 + 0.19x + x2 = 0 + 0.076 0.19x + x2 = 0 + 0.076 Combine like terms: 0 + 0.076 = 0.076 0.19x + x2 = 0.076 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 = 0.076 + 0.009025 Reorder the terms: 0.009025 + 0.19x + x2 = 0.076 + 0.009025 Combine like terms: 0.076 + 0.009025 = 0.085025 0.009025 + 0.19x + x2 = 0.085025 Factor a perfect square on the left side: (x + 0.095)(x + 0.095) = 0.085025 Calculate the square root of the right side: 0.291590466 Break this problem into two subproblems by setting (x + 0.095) equal to 0.291590466 and -0.291590466.Subproblem 1
x + 0.095 = 0.291590466 Simplifying x + 0.095 = 0.291590466 Reorder the terms: 0.095 + x = 0.291590466 Solving 0.095 + x = 0.291590466 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 = 0.291590466 + -0.095 Combine like terms: 0.095 + -0.095 = 0.000 0.000 + x = 0.291590466 + -0.095 x = 0.291590466 + -0.095 Combine like terms: 0.291590466 + -0.095 = 0.196590466 x = 0.196590466 Simplifying x = 0.196590466Subproblem 2
x + 0.095 = -0.291590466 Simplifying x + 0.095 = -0.291590466 Reorder the terms: 0.095 + x = -0.291590466 Solving 0.095 + x = -0.291590466 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 = -0.291590466 + -0.095 Combine like terms: 0.095 + -0.095 = 0.000 0.000 + x = -0.291590466 + -0.095 x = -0.291590466 + -0.095 Combine like terms: -0.291590466 + -0.095 = -0.386590466 x = -0.386590466 Simplifying x = -0.386590466Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.196590466, -0.386590466}
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