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Simplifying x2 + 4x + -10000 = 0 Reorder the terms: -10000 + 4x + x2 = 0 Solving -10000 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 4x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 4x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 4x + x2 = 0 + 10000 4x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 4x + x2 = 10000 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 10000 + 4 Reorder the terms: 4 + 4x + x2 = 10000 + 4 Combine like terms: 10000 + 4 = 10004 4 + 4x + x2 = 10004 Factor a perfect square on the left side: (x + 2)(x + 2) = 10004 Calculate the square root of the right side: 100.019998 Break this problem into two subproblems by setting (x + 2) equal to 100.019998 and -100.019998.Subproblem 1
x + 2 = 100.019998 Simplifying x + 2 = 100.019998 Reorder the terms: 2 + x = 100.019998 Solving 2 + x = 100.019998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 100.019998 + -2 Combine like terms: 2 + -2 = 0 0 + x = 100.019998 + -2 x = 100.019998 + -2 Combine like terms: 100.019998 + -2 = 98.019998 x = 98.019998 Simplifying x = 98.019998Subproblem 2
x + 2 = -100.019998 Simplifying x + 2 = -100.019998 Reorder the terms: 2 + x = -100.019998 Solving 2 + x = -100.019998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -100.019998 + -2 Combine like terms: 2 + -2 = 0 0 + x = -100.019998 + -2 x = -100.019998 + -2 Combine like terms: -100.019998 + -2 = -102.019998 x = -102.019998 Simplifying x = -102.019998Solution
The solution to the problem is based on the solutions from the subproblems. x = {98.019998, -102.019998}
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