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Simplifying 180x2 + -220x + 21 = 0 Reorder the terms: 21 + -220x + 180x2 = 0 Solving 21 + -220x + 180x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 180 the coefficient of the squared term: Divide each side by '180'. 0.1166666667 + -1.222222222x + x2 = 0 Move the constant term to the right: Add '-0.1166666667' to each side of the equation. 0.1166666667 + -1.222222222x + -0.1166666667 + x2 = 0 + -0.1166666667 Reorder the terms: 0.1166666667 + -0.1166666667 + -1.222222222x + x2 = 0 + -0.1166666667 Combine like terms: 0.1166666667 + -0.1166666667 = 0.0000000000 0.0000000000 + -1.222222222x + x2 = 0 + -0.1166666667 -1.222222222x + x2 = 0 + -0.1166666667 Combine like terms: 0 + -0.1166666667 = -0.1166666667 -1.222222222x + x2 = -0.1166666667 The x term is -1.222222222x. Take half its coefficient (-0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. -1.222222222x + 0.3734567900 + x2 = -0.1166666667 + 0.3734567900 Reorder the terms: 0.3734567900 + -1.222222222x + x2 = -0.1166666667 + 0.3734567900 Combine like terms: -0.1166666667 + 0.3734567900 = 0.2567901233 0.3734567900 + -1.222222222x + x2 = 0.2567901233 Factor a perfect square on the left side: (x + -0.611111111)(x + -0.611111111) = 0.2567901233 Calculate the square root of the right side: 0.506744633 Break this problem into two subproblems by setting (x + -0.611111111) equal to 0.506744633 and -0.506744633.Subproblem 1
x + -0.611111111 = 0.506744633 Simplifying x + -0.611111111 = 0.506744633 Reorder the terms: -0.611111111 + x = 0.506744633 Solving -0.611111111 + x = 0.506744633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + x = 0.506744633 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + x = 0.506744633 + 0.611111111 x = 0.506744633 + 0.611111111 Combine like terms: 0.506744633 + 0.611111111 = 1.117855744 x = 1.117855744 Simplifying x = 1.117855744Subproblem 2
x + -0.611111111 = -0.506744633 Simplifying x + -0.611111111 = -0.506744633 Reorder the terms: -0.611111111 + x = -0.506744633 Solving -0.611111111 + x = -0.506744633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.611111111' to each side of the equation. -0.611111111 + 0.611111111 + x = -0.506744633 + 0.611111111 Combine like terms: -0.611111111 + 0.611111111 = 0.000000000 0.000000000 + x = -0.506744633 + 0.611111111 x = -0.506744633 + 0.611111111 Combine like terms: -0.506744633 + 0.611111111 = 0.104366478 x = 0.104366478 Simplifying x = 0.104366478Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.117855744, 0.104366478}
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