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Simplifying 0.03x2 + -4x + 200 = 180 Reorder the terms: 200 + -4x + 0.03x2 = 180 Solving 200 + -4x + 0.03x2 = 180 Solving for variable 'x'. Reorder the terms: 200 + -180 + -4x + 0.03x2 = 180 + -180 Combine like terms: 200 + -180 = 20 20 + -4x + 0.03x2 = 180 + -180 Combine like terms: 180 + -180 = 0 20 + -4x + 0.03x2 = 0 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. 666.6666667 + -133.3333333x + x2 = 0 Move the constant term to the right: Add '-666.6666667' to each side of the equation. 666.6666667 + -133.3333333x + -666.6666667 + x2 = 0 + -666.6666667 Reorder the terms: 666.6666667 + -666.6666667 + -133.3333333x + x2 = 0 + -666.6666667 Combine like terms: 666.6666667 + -666.6666667 = 0.0000000 0.0000000 + -133.3333333x + x2 = 0 + -666.6666667 -133.3333333x + x2 = 0 + -666.6666667 Combine like terms: 0 + -666.6666667 = -666.6666667 -133.3333333x + x2 = -666.6666667 The x term is -133.3333333x. Take half its coefficient (-66.66666665). Square it (4444.444442) and add it to both sides. Add '4444.444442' to each side of the equation. -133.3333333x + 4444.444442 + x2 = -666.6666667 + 4444.444442 Reorder the terms: 4444.444442 + -133.3333333x + x2 = -666.6666667 + 4444.444442 Combine like terms: -666.6666667 + 4444.444442 = 3777.7777753 4444.444442 + -133.3333333x + x2 = 3777.7777753 Factor a perfect square on the left side: (x + -66.66666665)(x + -66.66666665) = 3777.7777753 Calculate the square root of the right side: 61.463629695 Break this problem into two subproblems by setting (x + -66.66666665) equal to 61.463629695 and -61.463629695.Subproblem 1
x + -66.66666665 = 61.463629695 Simplifying x + -66.66666665 = 61.463629695 Reorder the terms: -66.66666665 + x = 61.463629695 Solving -66.66666665 + x = 61.463629695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.66666665' to each side of the equation. -66.66666665 + 66.66666665 + x = 61.463629695 + 66.66666665 Combine like terms: -66.66666665 + 66.66666665 = 0.00000000 0.00000000 + x = 61.463629695 + 66.66666665 x = 61.463629695 + 66.66666665 Combine like terms: 61.463629695 + 66.66666665 = 128.130296345 x = 128.130296345 Simplifying x = 128.130296345Subproblem 2
x + -66.66666665 = -61.463629695 Simplifying x + -66.66666665 = -61.463629695 Reorder the terms: -66.66666665 + x = -61.463629695 Solving -66.66666665 + x = -61.463629695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.66666665' to each side of the equation. -66.66666665 + 66.66666665 + x = -61.463629695 + 66.66666665 Combine like terms: -66.66666665 + 66.66666665 = 0.00000000 0.00000000 + x = -61.463629695 + 66.66666665 x = -61.463629695 + 66.66666665 Combine like terms: -61.463629695 + 66.66666665 = 5.203036955 x = 5.203036955 Simplifying x = 5.203036955Solution
The solution to the problem is based on the solutions from the subproblems. x = {128.130296345, 5.203036955}
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