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Simplifying x2 + -6x + -4200 = 0 Reorder the terms: -4200 + -6x + x2 = 0 Solving -4200 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '4200' to each side of the equation. -4200 + -6x + 4200 + x2 = 0 + 4200 Reorder the terms: -4200 + 4200 + -6x + x2 = 0 + 4200 Combine like terms: -4200 + 4200 = 0 0 + -6x + x2 = 0 + 4200 -6x + x2 = 0 + 4200 Combine like terms: 0 + 4200 = 4200 -6x + x2 = 4200 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 = 4200 + 9 Reorder the terms: 9 + -6x + x2 = 4200 + 9 Combine like terms: 4200 + 9 = 4209 9 + -6x + x2 = 4209 Factor a perfect square on the left side: (x + -3)(x + -3) = 4209 Calculate the square root of the right side: 64.876806333 Break this problem into two subproblems by setting (x + -3) equal to 64.876806333 and -64.876806333.Subproblem 1
x + -3 = 64.876806333 Simplifying x + -3 = 64.876806333 Reorder the terms: -3 + x = 64.876806333 Solving -3 + x = 64.876806333 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 = 64.876806333 + 3 Combine like terms: -3 + 3 = 0 0 + x = 64.876806333 + 3 x = 64.876806333 + 3 Combine like terms: 64.876806333 + 3 = 67.876806333 x = 67.876806333 Simplifying x = 67.876806333Subproblem 2
x + -3 = -64.876806333 Simplifying x + -3 = -64.876806333 Reorder the terms: -3 + x = -64.876806333 Solving -3 + x = -64.876806333 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 = -64.876806333 + 3 Combine like terms: -3 + 3 = 0 0 + x = -64.876806333 + 3 x = -64.876806333 + 3 Combine like terms: -64.876806333 + 3 = -61.876806333 x = -61.876806333 Simplifying x = -61.876806333Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.876806333, -61.876806333}
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