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Simplifying (177x2 + 228x + 7075) + -1(255x2 + -2956x + 24336) = 0 Reorder the terms: (7075 + 228x + 177x2) + -1(255x2 + -2956x + 24336) = 0 Remove parenthesis around (7075 + 228x + 177x2) 7075 + 228x + 177x2 + -1(255x2 + -2956x + 24336) = 0 Reorder the terms: 7075 + 228x + 177x2 + -1(24336 + -2956x + 255x2) = 0 7075 + 228x + 177x2 + (24336 * -1 + -2956x * -1 + 255x2 * -1) = 0 7075 + 228x + 177x2 + (-24336 + 2956x + -255x2) = 0 Reorder the terms: 7075 + -24336 + 228x + 2956x + 177x2 + -255x2 = 0 Combine like terms: 7075 + -24336 = -17261 -17261 + 228x + 2956x + 177x2 + -255x2 = 0 Combine like terms: 228x + 2956x = 3184x -17261 + 3184x + 177x2 + -255x2 = 0 Combine like terms: 177x2 + -255x2 = -78x2 -17261 + 3184x + -78x2 = 0 Solving -17261 + 3184x + -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 + -40.82051282x + x2 = 0 Move the constant term to the right: Add '-221.2948718' to each side of the equation. 221.2948718 + -40.82051282x + -221.2948718 + x2 = 0 + -221.2948718 Reorder the terms: 221.2948718 + -221.2948718 + -40.82051282x + x2 = 0 + -221.2948718 Combine like terms: 221.2948718 + -221.2948718 = 0.0000000 0.0000000 + -40.82051282x + x2 = 0 + -221.2948718 -40.82051282x + x2 = 0 + -221.2948718 Combine like terms: 0 + -221.2948718 = -221.2948718 -40.82051282x + x2 = -221.2948718 The x term is -40.82051282x. Take half its coefficient (-20.41025641). Square it (416.5785667) and add it to both sides. Add '416.5785667' to each side of the equation. -40.82051282x + 416.5785667 + x2 = -221.2948718 + 416.5785667 Reorder the terms: 416.5785667 + -40.82051282x + x2 = -221.2948718 + 416.5785667 Combine like terms: -221.2948718 + 416.5785667 = 195.2836949 416.5785667 + -40.82051282x + x2 = 195.2836949 Factor a perfect square on the left side: (x + -20.41025641)(x + -20.41025641) = 195.2836949 Calculate the square root of the right side: 13.974394259 Break this problem into two subproblems by setting (x + -20.41025641) equal to 13.974394259 and -13.974394259.Subproblem 1
x + -20.41025641 = 13.974394259 Simplifying x + -20.41025641 = 13.974394259 Reorder the terms: -20.41025641 + x = 13.974394259 Solving -20.41025641 + x = 13.974394259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.41025641' to each side of the equation. -20.41025641 + 20.41025641 + x = 13.974394259 + 20.41025641 Combine like terms: -20.41025641 + 20.41025641 = 0.00000000 0.00000000 + x = 13.974394259 + 20.41025641 x = 13.974394259 + 20.41025641 Combine like terms: 13.974394259 + 20.41025641 = 34.384650669 x = 34.384650669 Simplifying x = 34.384650669Subproblem 2
x + -20.41025641 = -13.974394259 Simplifying x + -20.41025641 = -13.974394259 Reorder the terms: -20.41025641 + x = -13.974394259 Solving -20.41025641 + x = -13.974394259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20.41025641' to each side of the equation. -20.41025641 + 20.41025641 + x = -13.974394259 + 20.41025641 Combine like terms: -20.41025641 + 20.41025641 = 0.00000000 0.00000000 + x = -13.974394259 + 20.41025641 x = -13.974394259 + 20.41025641 Combine like terms: -13.974394259 + 20.41025641 = 6.435862151 x = 6.435862151 Simplifying x = 6.435862151Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.384650669, 6.435862151}
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