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Simplifying 0 = x2 + -110x + -2400 Reorder the terms: 0 = -2400 + -110x + x2 Solving 0 = -2400 + -110x + x2 Solving for variable 'x'. Combine like terms: 0 + 2400 = 2400 2400 + 110x + -1x2 = -2400 + -110x + x2 + 2400 + 110x + -1x2 Reorder the terms: 2400 + 110x + -1x2 = -2400 + 2400 + -110x + 110x + x2 + -1x2 Combine like terms: -2400 + 2400 = 0 2400 + 110x + -1x2 = 0 + -110x + 110x + x2 + -1x2 2400 + 110x + -1x2 = -110x + 110x + x2 + -1x2 Combine like terms: -110x + 110x = 0 2400 + 110x + -1x2 = 0 + x2 + -1x2 2400 + 110x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2400 + 110x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2400 + -110x + x2 = 0 Move the constant term to the right: Add '2400' to each side of the equation. -2400 + -110x + 2400 + x2 = 0 + 2400 Reorder the terms: -2400 + 2400 + -110x + x2 = 0 + 2400 Combine like terms: -2400 + 2400 = 0 0 + -110x + x2 = 0 + 2400 -110x + x2 = 0 + 2400 Combine like terms: 0 + 2400 = 2400 -110x + x2 = 2400 The x term is -110x. Take half its coefficient (-55). Square it (3025) and add it to both sides. Add '3025' to each side of the equation. -110x + 3025 + x2 = 2400 + 3025 Reorder the terms: 3025 + -110x + x2 = 2400 + 3025 Combine like terms: 2400 + 3025 = 5425 3025 + -110x + x2 = 5425 Factor a perfect square on the left side: (x + -55)(x + -55) = 5425 Calculate the square root of the right side: 73.654599313 Break this problem into two subproblems by setting (x + -55) equal to 73.654599313 and -73.654599313.Subproblem 1
x + -55 = 73.654599313 Simplifying x + -55 = 73.654599313 Reorder the terms: -55 + x = 73.654599313 Solving -55 + x = 73.654599313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = 73.654599313 + 55 Combine like terms: -55 + 55 = 0 0 + x = 73.654599313 + 55 x = 73.654599313 + 55 Combine like terms: 73.654599313 + 55 = 128.654599313 x = 128.654599313 Simplifying x = 128.654599313Subproblem 2
x + -55 = -73.654599313 Simplifying x + -55 = -73.654599313 Reorder the terms: -55 + x = -73.654599313 Solving -55 + x = -73.654599313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = -73.654599313 + 55 Combine like terms: -55 + 55 = 0 0 + x = -73.654599313 + 55 x = -73.654599313 + 55 Combine like terms: -73.654599313 + 55 = -18.654599313 x = -18.654599313 Simplifying x = -18.654599313Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.654599313, -18.654599313}
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