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Simplifying 18x2 + 7x + -72 = 0 Reorder the terms: -72 + 7x + 18x2 = 0 Solving -72 + 7x + 18x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -4 + 0.3888888889x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.3888888889x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 0.3888888889x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.3888888889x + x2 = 0 + 4 0.3888888889x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.3888888889x + x2 = 4 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 = 4 + 0.03780864200 Reorder the terms: 0.03780864200 + 0.3888888889x + x2 = 4 + 0.03780864200 Combine like terms: 4 + 0.03780864200 = 4.037808642 0.03780864200 + 0.3888888889x + x2 = 4.037808642 Factor a perfect square on the left side: (x + 0.1944444445)(x + 0.1944444445) = 4.037808642 Calculate the square root of the right side: 2.00942993 Break this problem into two subproblems by setting (x + 0.1944444445) equal to 2.00942993 and -2.00942993.Subproblem 1
x + 0.1944444445 = 2.00942993 Simplifying x + 0.1944444445 = 2.00942993 Reorder the terms: 0.1944444445 + x = 2.00942993 Solving 0.1944444445 + x = 2.00942993 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 = 2.00942993 + -0.1944444445 Combine like terms: 0.1944444445 + -0.1944444445 = 0.0000000000 0.0000000000 + x = 2.00942993 + -0.1944444445 x = 2.00942993 + -0.1944444445 Combine like terms: 2.00942993 + -0.1944444445 = 1.8149854855 x = 1.8149854855 Simplifying x = 1.8149854855Subproblem 2
x + 0.1944444445 = -2.00942993 Simplifying x + 0.1944444445 = -2.00942993 Reorder the terms: 0.1944444445 + x = -2.00942993 Solving 0.1944444445 + x = -2.00942993 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 = -2.00942993 + -0.1944444445 Combine like terms: 0.1944444445 + -0.1944444445 = 0.0000000000 0.0000000000 + x = -2.00942993 + -0.1944444445 x = -2.00942993 + -0.1944444445 Combine like terms: -2.00942993 + -0.1944444445 = -2.2038743745 x = -2.2038743745 Simplifying x = -2.2038743745Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8149854855, -2.2038743745}
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