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Simplifying x2 + 6x + -10000 = 0 Reorder the terms: -10000 + 6x + x2 = 0 Solving -10000 + 6x + 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 + 6x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 6x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 6x + x2 = 0 + 10000 6x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 6x + x2 = 10000 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 10000 + 9 Reorder the terms: 9 + 6x + x2 = 10000 + 9 Combine like terms: 10000 + 9 = 10009 9 + 6x + x2 = 10009 Factor a perfect square on the left side: (x + 3)(x + 3) = 10009 Calculate the square root of the right side: 100.04498988 Break this problem into two subproblems by setting (x + 3) equal to 100.04498988 and -100.04498988.Subproblem 1
x + 3 = 100.04498988 Simplifying x + 3 = 100.04498988 Reorder the terms: 3 + x = 100.04498988 Solving 3 + x = 100.04498988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 100.04498988 + -3 Combine like terms: 3 + -3 = 0 0 + x = 100.04498988 + -3 x = 100.04498988 + -3 Combine like terms: 100.04498988 + -3 = 97.04498988 x = 97.04498988 Simplifying x = 97.04498988Subproblem 2
x + 3 = -100.04498988 Simplifying x + 3 = -100.04498988 Reorder the terms: 3 + x = -100.04498988 Solving 3 + x = -100.04498988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -100.04498988 + -3 Combine like terms: 3 + -3 = 0 0 + x = -100.04498988 + -3 x = -100.04498988 + -3 Combine like terms: -100.04498988 + -3 = -103.04498988 x = -103.04498988 Simplifying x = -103.04498988Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.04498988, -103.04498988}
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