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Simplifying 2x(3x + 199) = 18 Reorder the terms: 2x(199 + 3x) = 18 (199 * 2x + 3x * 2x) = 18 (398x + 6x2) = 18 Solving 398x + 6x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + 398x + 6x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 398x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 199x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 199x + 3x2)' equal to zero and attempt to solve: Simplifying -9 + 199x + 3x2 = 0 Solving -9 + 199x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 66.33333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 66.33333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 66.33333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 66.33333333x + x2 = 0 + 3 66.33333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 66.33333333x + x2 = 3 The x term is 66.33333333x. Take half its coefficient (33.16666667). Square it (1100.027778) and add it to both sides. Add '1100.027778' to each side of the equation. 66.33333333x + 1100.027778 + x2 = 3 + 1100.027778 Reorder the terms: 1100.027778 + 66.33333333x + x2 = 3 + 1100.027778 Combine like terms: 3 + 1100.027778 = 1103.027778 1100.027778 + 66.33333333x + x2 = 1103.027778 Factor a perfect square on the left side: (x + 33.16666667)(x + 33.16666667) = 1103.027778 Calculate the square root of the right side: 33.211862007 Break this problem into two subproblems by setting (x + 33.16666667) equal to 33.211862007 and -33.211862007.Subproblem 1
x + 33.16666667 = 33.211862007 Simplifying x + 33.16666667 = 33.211862007 Reorder the terms: 33.16666667 + x = 33.211862007 Solving 33.16666667 + x = 33.211862007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33.16666667' to each side of the equation. 33.16666667 + -33.16666667 + x = 33.211862007 + -33.16666667 Combine like terms: 33.16666667 + -33.16666667 = 0.00000000 0.00000000 + x = 33.211862007 + -33.16666667 x = 33.211862007 + -33.16666667 Combine like terms: 33.211862007 + -33.16666667 = 0.045195337 x = 0.045195337 Simplifying x = 0.045195337Subproblem 2
x + 33.16666667 = -33.211862007 Simplifying x + 33.16666667 = -33.211862007 Reorder the terms: 33.16666667 + x = -33.211862007 Solving 33.16666667 + x = -33.211862007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-33.16666667' to each side of the equation. 33.16666667 + -33.16666667 + x = -33.211862007 + -33.16666667 Combine like terms: 33.16666667 + -33.16666667 = 0.00000000 0.00000000 + x = -33.211862007 + -33.16666667 x = -33.211862007 + -33.16666667 Combine like terms: -33.211862007 + -33.16666667 = -66.378528677 x = -66.378528677 Simplifying x = -66.378528677Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.045195337, -66.378528677}Solution
x = {0.045195337, -66.378528677}
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