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Simplifying x2 + -12x + -600 = 0 Reorder the terms: -600 + -12x + x2 = 0 Solving -600 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '600' to each side of the equation. -600 + -12x + 600 + x2 = 0 + 600 Reorder the terms: -600 + 600 + -12x + x2 = 0 + 600 Combine like terms: -600 + 600 = 0 0 + -12x + x2 = 0 + 600 -12x + x2 = 0 + 600 Combine like terms: 0 + 600 = 600 -12x + x2 = 600 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 600 + 36 Reorder the terms: 36 + -12x + x2 = 600 + 36 Combine like terms: 600 + 36 = 636 36 + -12x + x2 = 636 Factor a perfect square on the left side: (x + -6)(x + -6) = 636 Calculate the square root of the right side: 25.219040426 Break this problem into two subproblems by setting (x + -6) equal to 25.219040426 and -25.219040426.Subproblem 1
x + -6 = 25.219040426 Simplifying x + -6 = 25.219040426 Reorder the terms: -6 + x = 25.219040426 Solving -6 + x = 25.219040426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 25.219040426 + 6 Combine like terms: -6 + 6 = 0 0 + x = 25.219040426 + 6 x = 25.219040426 + 6 Combine like terms: 25.219040426 + 6 = 31.219040426 x = 31.219040426 Simplifying x = 31.219040426Subproblem 2
x + -6 = -25.219040426 Simplifying x + -6 = -25.219040426 Reorder the terms: -6 + x = -25.219040426 Solving -6 + x = -25.219040426 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -25.219040426 + 6 Combine like terms: -6 + 6 = 0 0 + x = -25.219040426 + 6 x = -25.219040426 + 6 Combine like terms: -25.219040426 + 6 = -19.219040426 x = -19.219040426 Simplifying x = -19.219040426Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.219040426, -19.219040426}
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