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Simplifying x2 + -0.4x = 7980 Reorder the terms: -0.4x + x2 = 7980 Solving -0.4x + x2 = 7980 Solving for variable 'x'. Reorder the terms: -7980 + -0.4x + x2 = 7980 + -7980 Combine like terms: 7980 + -7980 = 0 -7980 + -0.4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7980' to each side of the equation. -7980 + -0.4x + 7980 + x2 = 0 + 7980 Reorder the terms: -7980 + 7980 + -0.4x + x2 = 0 + 7980 Combine like terms: -7980 + 7980 = 0 0 + -0.4x + x2 = 0 + 7980 -0.4x + x2 = 0 + 7980 Combine like terms: 0 + 7980 = 7980 -0.4x + x2 = 7980 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 7980 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 7980 + 0.04 Combine like terms: 7980 + 0.04 = 7980.04 0.04 + -0.4x + x2 = 7980.04 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 7980.04 Calculate the square root of the right side: 89.331069623 Break this problem into two subproblems by setting (x + -0.2) equal to 89.331069623 and -89.331069623.Subproblem 1
x + -0.2 = 89.331069623 Simplifying x + -0.2 = 89.331069623 Reorder the terms: -0.2 + x = 89.331069623 Solving -0.2 + x = 89.331069623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 89.331069623 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 89.331069623 + 0.2 x = 89.331069623 + 0.2 Combine like terms: 89.331069623 + 0.2 = 89.531069623 x = 89.531069623 Simplifying x = 89.531069623Subproblem 2
x + -0.2 = -89.331069623 Simplifying x + -0.2 = -89.331069623 Reorder the terms: -0.2 + x = -89.331069623 Solving -0.2 + x = -89.331069623 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -89.331069623 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -89.331069623 + 0.2 x = -89.331069623 + 0.2 Combine like terms: -89.331069623 + 0.2 = -89.131069623 x = -89.131069623 Simplifying x = -89.131069623Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.531069623, -89.131069623}
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