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Simplifying 500 + -2x + -5x2 = 0 Solving 500 + -2x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -100 + 0.4x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 0.4x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 0.4x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 0.4x + x2 = 0 + 100 0.4x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 0.4x + x2 = 100 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 = 100 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 100 + 0.04 Combine like terms: 100 + 0.04 = 100.04 0.04 + 0.4x + x2 = 100.04 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 100.04 Calculate the square root of the right side: 10.0019998 Break this problem into two subproblems by setting (x + 0.2) equal to 10.0019998 and -10.0019998.Subproblem 1
x + 0.2 = 10.0019998 Simplifying x + 0.2 = 10.0019998 Reorder the terms: 0.2 + x = 10.0019998 Solving 0.2 + x = 10.0019998 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 = 10.0019998 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 10.0019998 + -0.2 x = 10.0019998 + -0.2 Combine like terms: 10.0019998 + -0.2 = 9.8019998 x = 9.8019998 Simplifying x = 9.8019998Subproblem 2
x + 0.2 = -10.0019998 Simplifying x + 0.2 = -10.0019998 Reorder the terms: 0.2 + x = -10.0019998 Solving 0.2 + x = -10.0019998 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 = -10.0019998 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -10.0019998 + -0.2 x = -10.0019998 + -0.2 Combine like terms: -10.0019998 + -0.2 = -10.2019998 x = -10.2019998 Simplifying x = -10.2019998Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.8019998, -10.2019998}
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