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Simplifying 10800 = x2 + 30x + 35 Reorder the terms: 10800 = 35 + 30x + x2 Solving 10800 = 35 + 30x + x2 Solving for variable 'x'. Combine like terms: 10800 + -35 = 10765 10765 + -30x + -1x2 = 35 + 30x + x2 + -35 + -30x + -1x2 Reorder the terms: 10765 + -30x + -1x2 = 35 + -35 + 30x + -30x + x2 + -1x2 Combine like terms: 35 + -35 = 0 10765 + -30x + -1x2 = 0 + 30x + -30x + x2 + -1x2 10765 + -30x + -1x2 = 30x + -30x + x2 + -1x2 Combine like terms: 30x + -30x = 0 10765 + -30x + -1x2 = 0 + x2 + -1x2 10765 + -30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10765 + -30x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10765 + 30x + x2 = 0 Move the constant term to the right: Add '10765' to each side of the equation. -10765 + 30x + 10765 + x2 = 0 + 10765 Reorder the terms: -10765 + 10765 + 30x + x2 = 0 + 10765 Combine like terms: -10765 + 10765 = 0 0 + 30x + x2 = 0 + 10765 30x + x2 = 0 + 10765 Combine like terms: 0 + 10765 = 10765 30x + x2 = 10765 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 10765 + 225 Reorder the terms: 225 + 30x + x2 = 10765 + 225 Combine like terms: 10765 + 225 = 10990 225 + 30x + x2 = 10990 Factor a perfect square on the left side: (x + 15)(x + 15) = 10990 Calculate the square root of the right side: 104.833200848 Break this problem into two subproblems by setting (x + 15) equal to 104.833200848 and -104.833200848.Subproblem 1
x + 15 = 104.833200848 Simplifying x + 15 = 104.833200848 Reorder the terms: 15 + x = 104.833200848 Solving 15 + x = 104.833200848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 104.833200848 + -15 Combine like terms: 15 + -15 = 0 0 + x = 104.833200848 + -15 x = 104.833200848 + -15 Combine like terms: 104.833200848 + -15 = 89.833200848 x = 89.833200848 Simplifying x = 89.833200848Subproblem 2
x + 15 = -104.833200848 Simplifying x + 15 = -104.833200848 Reorder the terms: 15 + x = -104.833200848 Solving 15 + x = -104.833200848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -104.833200848 + -15 Combine like terms: 15 + -15 = 0 0 + x = -104.833200848 + -15 x = -104.833200848 + -15 Combine like terms: -104.833200848 + -15 = -119.833200848 x = -119.833200848 Simplifying x = -119.833200848Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.833200848, -119.833200848}
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