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Simplifying 3(90 + -1x(180 + -1x)) = 10 3(90 + (180 * -1x + -1x * -1x)) = 10 3(90 + (-180x + 1x2)) = 10 (90 * 3 + -180x * 3 + 1x2 * 3) = 10 (270 + -540x + 3x2) = 10 Solving 270 + -540x + 3x2 = 10 Solving for variable 'x'. Reorder the terms: 270 + -10 + -540x + 3x2 = 10 + -10 Combine like terms: 270 + -10 = 260 260 + -540x + 3x2 = 10 + -10 Combine like terms: 10 + -10 = 0 260 + -540x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 86.66666667 + -180x + x2 = 0 Move the constant term to the right: Add '-86.66666667' to each side of the equation. 86.66666667 + -180x + -86.66666667 + x2 = 0 + -86.66666667 Reorder the terms: 86.66666667 + -86.66666667 + -180x + x2 = 0 + -86.66666667 Combine like terms: 86.66666667 + -86.66666667 = 0.00000000 0.00000000 + -180x + x2 = 0 + -86.66666667 -180x + x2 = 0 + -86.66666667 Combine like terms: 0 + -86.66666667 = -86.66666667 -180x + x2 = -86.66666667 The x term is -180x. Take half its coefficient (-90). Square it (8100) and add it to both sides. Add '8100' to each side of the equation. -180x + 8100 + x2 = -86.66666667 + 8100 Reorder the terms: 8100 + -180x + x2 = -86.66666667 + 8100 Combine like terms: -86.66666667 + 8100 = 8013.33333333 8100 + -180x + x2 = 8013.33333333 Factor a perfect square on the left side: (x + -90)(x + -90) = 8013.33333333 Calculate the square root of the right side: 89.517223669 Break this problem into two subproblems by setting (x + -90) equal to 89.517223669 and -89.517223669.Subproblem 1
x + -90 = 89.517223669 Simplifying x + -90 = 89.517223669 Reorder the terms: -90 + x = 89.517223669 Solving -90 + x = 89.517223669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = 89.517223669 + 90 Combine like terms: -90 + 90 = 0 0 + x = 89.517223669 + 90 x = 89.517223669 + 90 Combine like terms: 89.517223669 + 90 = 179.517223669 x = 179.517223669 Simplifying x = 179.517223669Subproblem 2
x + -90 = -89.517223669 Simplifying x + -90 = -89.517223669 Reorder the terms: -90 + x = -89.517223669 Solving -90 + x = -89.517223669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + x = -89.517223669 + 90 Combine like terms: -90 + 90 = 0 0 + x = -89.517223669 + 90 x = -89.517223669 + 90 Combine like terms: -89.517223669 + 90 = 0.482776331 x = 0.482776331 Simplifying x = 0.482776331Solution
The solution to the problem is based on the solutions from the subproblems. x = {179.517223669, 0.482776331}
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