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Simplifying 0 = x2 + 12x + -600 Reorder the terms: 0 = -600 + 12x + x2 Solving 0 = -600 + 12x + x2 Solving for variable 'x'. Combine like terms: 0 + 600 = 600 600 + -12x + -1x2 = -600 + 12x + x2 + 600 + -12x + -1x2 Reorder the terms: 600 + -12x + -1x2 = -600 + 600 + 12x + -12x + x2 + -1x2 Combine like terms: -600 + 600 = 0 600 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2 600 + -12x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 600 + -12x + -1x2 = 0 + x2 + -1x2 600 + -12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 600 + -12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -600 + 12x + x2 = 0 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 = 19.219040426 x = 19.219040426 Simplifying x = 19.219040426Subproblem 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 = -31.219040426 x = -31.219040426 Simplifying x = -31.219040426Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.219040426, -31.219040426}
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