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Simplifying 60x + 800 = 1000x + -3x2 Reorder the terms: 800 + 60x = 1000x + -3x2 Solving 800 + 60x = 1000x + -3x2 Solving for variable 'x'. Combine like terms: 60x + -1000x = -940x 800 + -940x + 3x2 = 1000x + -3x2 + -1000x + 3x2 Reorder the terms: 800 + -940x + 3x2 = 1000x + -1000x + -3x2 + 3x2 Combine like terms: 1000x + -1000x = 0 800 + -940x + 3x2 = 0 + -3x2 + 3x2 800 + -940x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 800 + -940x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 266.6666667 + -313.3333333x + x2 = 0 Move the constant term to the right: Add '-266.6666667' to each side of the equation. 266.6666667 + -313.3333333x + -266.6666667 + x2 = 0 + -266.6666667 Reorder the terms: 266.6666667 + -266.6666667 + -313.3333333x + x2 = 0 + -266.6666667 Combine like terms: 266.6666667 + -266.6666667 = 0.0000000 0.0000000 + -313.3333333x + x2 = 0 + -266.6666667 -313.3333333x + x2 = 0 + -266.6666667 Combine like terms: 0 + -266.6666667 = -266.6666667 -313.3333333x + x2 = -266.6666667 The x term is -313.3333333x. Take half its coefficient (-156.6666667). Square it (24544.44445) and add it to both sides. Add '24544.44445' to each side of the equation. -313.3333333x + 24544.44445 + x2 = -266.6666667 + 24544.44445 Reorder the terms: 24544.44445 + -313.3333333x + x2 = -266.6666667 + 24544.44445 Combine like terms: -266.6666667 + 24544.44445 = 24277.7777833 24544.44445 + -313.3333333x + x2 = 24277.7777833 Factor a perfect square on the left side: (x + -156.6666667)(x + -156.6666667) = 24277.7777833 Calculate the square root of the right side: 155.813278585 Break this problem into two subproblems by setting (x + -156.6666667) equal to 155.813278585 and -155.813278585.Subproblem 1
x + -156.6666667 = 155.813278585 Simplifying x + -156.6666667 = 155.813278585 Reorder the terms: -156.6666667 + x = 155.813278585 Solving -156.6666667 + x = 155.813278585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '156.6666667' to each side of the equation. -156.6666667 + 156.6666667 + x = 155.813278585 + 156.6666667 Combine like terms: -156.6666667 + 156.6666667 = 0.0000000 0.0000000 + x = 155.813278585 + 156.6666667 x = 155.813278585 + 156.6666667 Combine like terms: 155.813278585 + 156.6666667 = 312.479945285 x = 312.479945285 Simplifying x = 312.479945285Subproblem 2
x + -156.6666667 = -155.813278585 Simplifying x + -156.6666667 = -155.813278585 Reorder the terms: -156.6666667 + x = -155.813278585 Solving -156.6666667 + x = -155.813278585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '156.6666667' to each side of the equation. -156.6666667 + 156.6666667 + x = -155.813278585 + 156.6666667 Combine like terms: -156.6666667 + 156.6666667 = 0.0000000 0.0000000 + x = -155.813278585 + 156.6666667 x = -155.813278585 + 156.6666667 Combine like terms: -155.813278585 + 156.6666667 = 0.853388115 x = 0.853388115 Simplifying x = 0.853388115Solution
The solution to the problem is based on the solutions from the subproblems. x = {312.479945285, 0.853388115}
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