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Simplifying 8800 = x2 + 30x + -7000 Reorder the terms: 8800 = -7000 + 30x + x2 Solving 8800 = -7000 + 30x + x2 Solving for variable 'x'. Combine like terms: 8800 + 7000 = 15800 15800 + -30x + -1x2 = -7000 + 30x + x2 + 7000 + -30x + -1x2 Reorder the terms: 15800 + -30x + -1x2 = -7000 + 7000 + 30x + -30x + x2 + -1x2 Combine like terms: -7000 + 7000 = 0 15800 + -30x + -1x2 = 0 + 30x + -30x + x2 + -1x2 15800 + -30x + -1x2 = 30x + -30x + x2 + -1x2 Combine like terms: 30x + -30x = 0 15800 + -30x + -1x2 = 0 + x2 + -1x2 15800 + -30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15800 + -30x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15800 + 30x + x2 = 0 Move the constant term to the right: Add '15800' to each side of the equation. -15800 + 30x + 15800 + x2 = 0 + 15800 Reorder the terms: -15800 + 15800 + 30x + x2 = 0 + 15800 Combine like terms: -15800 + 15800 = 0 0 + 30x + x2 = 0 + 15800 30x + x2 = 0 + 15800 Combine like terms: 0 + 15800 = 15800 30x + x2 = 15800 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 = 15800 + 225 Reorder the terms: 225 + 30x + x2 = 15800 + 225 Combine like terms: 15800 + 225 = 16025 225 + 30x + x2 = 16025 Factor a perfect square on the left side: (x + 15)(x + 15) = 16025 Calculate the square root of the right side: 126.589889012 Break this problem into two subproblems by setting (x + 15) equal to 126.589889012 and -126.589889012.Subproblem 1
x + 15 = 126.589889012 Simplifying x + 15 = 126.589889012 Reorder the terms: 15 + x = 126.589889012 Solving 15 + x = 126.589889012 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 = 126.589889012 + -15 Combine like terms: 15 + -15 = 0 0 + x = 126.589889012 + -15 x = 126.589889012 + -15 Combine like terms: 126.589889012 + -15 = 111.589889012 x = 111.589889012 Simplifying x = 111.589889012Subproblem 2
x + 15 = -126.589889012 Simplifying x + 15 = -126.589889012 Reorder the terms: 15 + x = -126.589889012 Solving 15 + x = -126.589889012 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 = -126.589889012 + -15 Combine like terms: 15 + -15 = 0 0 + x = -126.589889012 + -15 x = -126.589889012 + -15 Combine like terms: -126.589889012 + -15 = -141.589889012 x = -141.589889012 Simplifying x = -141.589889012Solution
The solution to the problem is based on the solutions from the subproblems. x = {111.589889012, -141.589889012}
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