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Simplifying (177x2 + 288x + 7075) + -1(255x2 + -2956x + 24336) = 0 Reorder the terms: (7075 + 288x + 177x2) + -1(255x2 + -2956x + 24336) = 0 Remove parenthesis around (7075 + 288x + 177x2) 7075 + 288x + 177x2 + -1(255x2 + -2956x + 24336) = 0 Reorder the terms: 7075 + 288x + 177x2 + -1(24336 + -2956x + 255x2) = 0 7075 + 288x + 177x2 + (24336 * -1 + -2956x * -1 + 255x2 * -1) = 0 7075 + 288x + 177x2 + (-24336 + 2956x + -255x2) = 0 Reorder the terms: 7075 + -24336 + 288x + 2956x + 177x2 + -255x2 = 0 Combine like terms: 7075 + -24336 = -17261 -17261 + 288x + 2956x + 177x2 + -255x2 = 0 Combine like terms: 288x + 2956x = 3244x -17261 + 3244x + 177x2 + -255x2 = 0 Combine like terms: 177x2 + -255x2 = -78x2 -17261 + 3244x + -78x2 = 0 Solving -17261 + 3244x + -78x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -78 the coefficient of the squared term: Divide each side by '-78'. 221.2948718 + -41.58974359x + x2 = 0 Move the constant term to the right: Add '-221.2948718' to each side of the equation. 221.2948718 + -41.58974359x + -221.2948718 + x2 = 0 + -221.2948718 Reorder the terms: 221.2948718 + -221.2948718 + -41.58974359x + x2 = 0 + -221.2948718 Combine like terms: 221.2948718 + -221.2948718 = 0.0000000 0.0000000 + -41.58974359x + x2 = 0 + -221.2948718 -41.58974359x + x2 = 0 + -221.2948718 Combine like terms: 0 + -221.2948718 = -221.2948718 -41.58974359x + x2 = -221.2948718 The x term is -41.58974359x. Take half its coefficient (-20.7948718). Square it (432.4266932) and add it to both sides. Add '432.4266932' to each side of the equation. -41.58974359x + 432.4266932 + x2 = -221.2948718 + 432.4266932 Reorder the terms: 432.4266932 + -41.58974359x + x2 = -221.2948718 + 432.4266932 Combine like terms: -221.2948718 + 432.4266932 = 211.1318214 432.4266932 + -41.58974359x + x2 = 211.1318214 Factor a perfect square on the left side: (x + -20.7948718)(x + -20.7948718) = 211.1318214 Calculate the square root of the right side: 14.530375818 Break this problem into two subproblems by setting (x + -20.7948718) equal to 14.530375818 and -14.530375818.Subproblem 1
x + -20.7948718 = 14.530375818 Simplifying x + -20.7948718 = 14.530375818 Reorder the terms: -20.7948718 + x = 14.530375818 Solving -20.7948718 + x = 14.530375818 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.7948718' to each side of the equation. -20.7948718 + 20.7948718 + x = 14.530375818 + 20.7948718 Combine like terms: -20.7948718 + 20.7948718 = 0.0000000 0.0000000 + x = 14.530375818 + 20.7948718 x = 14.530375818 + 20.7948718 Combine like terms: 14.530375818 + 20.7948718 = 35.325247618 x = 35.325247618 Simplifying x = 35.325247618Subproblem 2
x + -20.7948718 = -14.530375818 Simplifying x + -20.7948718 = -14.530375818 Reorder the terms: -20.7948718 + x = -14.530375818 Solving -20.7948718 + x = -14.530375818 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.7948718' to each side of the equation. -20.7948718 + 20.7948718 + x = -14.530375818 + 20.7948718 Combine like terms: -20.7948718 + 20.7948718 = 0.0000000 0.0000000 + x = -14.530375818 + 20.7948718 x = -14.530375818 + 20.7948718 Combine like terms: -14.530375818 + 20.7948718 = 6.264495982 x = 6.264495982 Simplifying x = 6.264495982Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.325247618, 6.264495982}
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