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Simplifying 8800 = x2 + -30x + 700 Reorder the terms: 8800 = 700 + -30x + x2 Solving 8800 = 700 + -30x + x2 Solving for variable 'x'. Combine like terms: 8800 + -700 = 8100 8100 + 30x + -1x2 = 700 + -30x + x2 + -700 + 30x + -1x2 Reorder the terms: 8100 + 30x + -1x2 = 700 + -700 + -30x + 30x + x2 + -1x2 Combine like terms: 700 + -700 = 0 8100 + 30x + -1x2 = 0 + -30x + 30x + x2 + -1x2 8100 + 30x + -1x2 = -30x + 30x + x2 + -1x2 Combine like terms: -30x + 30x = 0 8100 + 30x + -1x2 = 0 + x2 + -1x2 8100 + 30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8100 + 30x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8100 + -30x + x2 = 0 Move the constant term to the right: Add '8100' to each side of the equation. -8100 + -30x + 8100 + x2 = 0 + 8100 Reorder the terms: -8100 + 8100 + -30x + x2 = 0 + 8100 Combine like terms: -8100 + 8100 = 0 0 + -30x + x2 = 0 + 8100 -30x + x2 = 0 + 8100 Combine like terms: 0 + 8100 = 8100 -30x + x2 = 8100 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 = 8100 + 225 Reorder the terms: 225 + -30x + x2 = 8100 + 225 Combine like terms: 8100 + 225 = 8325 225 + -30x + x2 = 8325 Factor a perfect square on the left side: (x + -15)(x + -15) = 8325 Calculate the square root of the right side: 91.241437954 Break this problem into two subproblems by setting (x + -15) equal to 91.241437954 and -91.241437954.Subproblem 1
x + -15 = 91.241437954 Simplifying x + -15 = 91.241437954 Reorder the terms: -15 + x = 91.241437954 Solving -15 + x = 91.241437954 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 = 91.241437954 + 15 Combine like terms: -15 + 15 = 0 0 + x = 91.241437954 + 15 x = 91.241437954 + 15 Combine like terms: 91.241437954 + 15 = 106.241437954 x = 106.241437954 Simplifying x = 106.241437954Subproblem 2
x + -15 = -91.241437954 Simplifying x + -15 = -91.241437954 Reorder the terms: -15 + x = -91.241437954 Solving -15 + x = -91.241437954 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 = -91.241437954 + 15 Combine like terms: -15 + 15 = 0 0 + x = -91.241437954 + 15 x = -91.241437954 + 15 Combine like terms: -91.241437954 + 15 = -76.241437954 x = -76.241437954 Simplifying x = -76.241437954Solution
The solution to the problem is based on the solutions from the subproblems. x = {106.241437954, -76.241437954}
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