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Simplifying 18x2 + 7x = 180 Reorder the terms: 7x + 18x2 = 180 Solving 7x + 18x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 7x + 18x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 7x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -10 + 0.3888888889x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 0.3888888889x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 0.3888888889x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 0.3888888889x + x2 = 0 + 10 0.3888888889x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 0.3888888889x + x2 = 10 The x term is 0.3888888889x. Take half its coefficient (0.1944444445). Square it (0.03780864200) and add it to both sides. Add '0.03780864200' to each side of the equation. 0.3888888889x + 0.03780864200 + x2 = 10 + 0.03780864200 Reorder the terms: 0.03780864200 + 0.3888888889x + x2 = 10 + 0.03780864200 Combine like terms: 10 + 0.03780864200 = 10.037808642 0.03780864200 + 0.3888888889x + x2 = 10.037808642 Factor a perfect square on the left side: (x + 0.1944444445)(x + 0.1944444445) = 10.037808642 Calculate the square root of the right side: 3.168250091 Break this problem into two subproblems by setting (x + 0.1944444445) equal to 3.168250091 and -3.168250091.Subproblem 1
x + 0.1944444445 = 3.168250091 Simplifying x + 0.1944444445 = 3.168250091 Reorder the terms: 0.1944444445 + x = 3.168250091 Solving 0.1944444445 + x = 3.168250091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1944444445' to each side of the equation. 0.1944444445 + -0.1944444445 + x = 3.168250091 + -0.1944444445 Combine like terms: 0.1944444445 + -0.1944444445 = 0.0000000000 0.0000000000 + x = 3.168250091 + -0.1944444445 x = 3.168250091 + -0.1944444445 Combine like terms: 3.168250091 + -0.1944444445 = 2.9738056465 x = 2.9738056465 Simplifying x = 2.9738056465Subproblem 2
x + 0.1944444445 = -3.168250091 Simplifying x + 0.1944444445 = -3.168250091 Reorder the terms: 0.1944444445 + x = -3.168250091 Solving 0.1944444445 + x = -3.168250091 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1944444445' to each side of the equation. 0.1944444445 + -0.1944444445 + x = -3.168250091 + -0.1944444445 Combine like terms: 0.1944444445 + -0.1944444445 = 0.0000000000 0.0000000000 + x = -3.168250091 + -0.1944444445 x = -3.168250091 + -0.1944444445 Combine like terms: -3.168250091 + -0.1944444445 = -3.3626945355 x = -3.3626945355 Simplifying x = -3.3626945355Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9738056465, -3.3626945355}
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