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Simplifying 324423x + 222222x2 + -53274 = 213234 Reorder the terms: -53274 + 324423x + 222222x2 = 213234 Solving -53274 + 324423x + 222222x2 = 213234 Solving for variable 'x'. Reorder the terms: -53274 + -213234 + 324423x + 222222x2 = 213234 + -213234 Combine like terms: -53274 + -213234 = -266508 -266508 + 324423x + 222222x2 = 213234 + -213234 Combine like terms: 213234 + -213234 = 0 -266508 + 324423x + 222222x2 = 0 Factor out the Greatest Common Factor (GCF), '33'. 33(-8076 + 9831x + 6734x2) = 0 Ignore the factor 33.Subproblem 1
Set the factor '(-8076 + 9831x + 6734x2)' equal to zero and attempt to solve: Simplifying -8076 + 9831x + 6734x2 = 0 Solving -8076 + 9831x + 6734x2 = 0 Begin completing the square. Divide all terms by 6734 the coefficient of the squared term: Divide each side by '6734'. -1.199287199 + 1.45990496x + x2 = 0 Move the constant term to the right: Add '1.199287199' to each side of the equation. -1.199287199 + 1.45990496x + 1.199287199 + x2 = 0 + 1.199287199 Reorder the terms: -1.199287199 + 1.199287199 + 1.45990496x + x2 = 0 + 1.199287199 Combine like terms: -1.199287199 + 1.199287199 = 0.000000000 0.000000000 + 1.45990496x + x2 = 0 + 1.199287199 1.45990496x + x2 = 0 + 1.199287199 Combine like terms: 0 + 1.199287199 = 1.199287199 1.45990496x + x2 = 1.199287199 The x term is 1.45990496x. Take half its coefficient (0.72995248). Square it (0.5328306231) and add it to both sides. Add '0.5328306231' to each side of the equation. 1.45990496x + 0.5328306231 + x2 = 1.199287199 + 0.5328306231 Reorder the terms: 0.5328306231 + 1.45990496x + x2 = 1.199287199 + 0.5328306231 Combine like terms: 1.199287199 + 0.5328306231 = 1.7321178221 0.5328306231 + 1.45990496x + x2 = 1.7321178221 Factor a perfect square on the left side: (x + 0.72995248)(x + 0.72995248) = 1.7321178221 Calculate the square root of the right side: 1.316099473 Break this problem into two subproblems by setting (x + 0.72995248) equal to 1.316099473 and -1.316099473.Subproblem 1
x + 0.72995248 = 1.316099473 Simplifying x + 0.72995248 = 1.316099473 Reorder the terms: 0.72995248 + x = 1.316099473 Solving 0.72995248 + x = 1.316099473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.72995248' to each side of the equation. 0.72995248 + -0.72995248 + x = 1.316099473 + -0.72995248 Combine like terms: 0.72995248 + -0.72995248 = 0.00000000 0.00000000 + x = 1.316099473 + -0.72995248 x = 1.316099473 + -0.72995248 Combine like terms: 1.316099473 + -0.72995248 = 0.586146993 x = 0.586146993 Simplifying x = 0.586146993Subproblem 2
x + 0.72995248 = -1.316099473 Simplifying x + 0.72995248 = -1.316099473 Reorder the terms: 0.72995248 + x = -1.316099473 Solving 0.72995248 + x = -1.316099473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.72995248' to each side of the equation. 0.72995248 + -0.72995248 + x = -1.316099473 + -0.72995248 Combine like terms: 0.72995248 + -0.72995248 = 0.00000000 0.00000000 + x = -1.316099473 + -0.72995248 x = -1.316099473 + -0.72995248 Combine like terms: -1.316099473 + -0.72995248 = -2.046051953 x = -2.046051953 Simplifying x = -2.046051953Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.586146993, -2.046051953}Solution
x = {0.586146993, -2.046051953}
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