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Simplifying 18x2 + 7x + -21 = 0 Reorder the terms: -21 + 7x + 18x2 = 0 Solving -21 + 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'. -1.166666667 + 0.3888888889x + x2 = 0 Move the constant term to the right: Add '1.166666667' to each side of the equation. -1.166666667 + 0.3888888889x + 1.166666667 + x2 = 0 + 1.166666667 Reorder the terms: -1.166666667 + 1.166666667 + 0.3888888889x + x2 = 0 + 1.166666667 Combine like terms: -1.166666667 + 1.166666667 = 0.000000000 0.000000000 + 0.3888888889x + x2 = 0 + 1.166666667 0.3888888889x + x2 = 0 + 1.166666667 Combine like terms: 0 + 1.166666667 = 1.166666667 0.3888888889x + x2 = 1.166666667 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 = 1.166666667 + 0.03780864200 Reorder the terms: 0.03780864200 + 0.3888888889x + x2 = 1.166666667 + 0.03780864200 Combine like terms: 1.166666667 + 0.03780864200 = 1.204475309 0.03780864200 + 0.3888888889x + x2 = 1.204475309 Factor a perfect square on the left side: (x + 0.1944444445)(x + 0.1944444445) = 1.204475309 Calculate the square root of the right side: 1.097485904 Break this problem into two subproblems by setting (x + 0.1944444445) equal to 1.097485904 and -1.097485904.Subproblem 1
x + 0.1944444445 = 1.097485904 Simplifying x + 0.1944444445 = 1.097485904 Reorder the terms: 0.1944444445 + x = 1.097485904 Solving 0.1944444445 + x = 1.097485904 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 = 1.097485904 + -0.1944444445 Combine like terms: 0.1944444445 + -0.1944444445 = 0.0000000000 0.0000000000 + x = 1.097485904 + -0.1944444445 x = 1.097485904 + -0.1944444445 Combine like terms: 1.097485904 + -0.1944444445 = 0.9030414595 x = 0.9030414595 Simplifying x = 0.9030414595Subproblem 2
x + 0.1944444445 = -1.097485904 Simplifying x + 0.1944444445 = -1.097485904 Reorder the terms: 0.1944444445 + x = -1.097485904 Solving 0.1944444445 + x = -1.097485904 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 = -1.097485904 + -0.1944444445 Combine like terms: 0.1944444445 + -0.1944444445 = 0.0000000000 0.0000000000 + x = -1.097485904 + -0.1944444445 x = -1.097485904 + -0.1944444445 Combine like terms: -1.097485904 + -0.1944444445 = -1.2919303485 x = -1.2919303485 Simplifying x = -1.2919303485Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9030414595, -1.2919303485}
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