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Simplifying 9x2 + 28x + -240 = 0 Reorder the terms: -240 + 28x + 9x2 = 0 Solving -240 + 28x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -26.66666667 + 3.111111111x + x2 = 0 Move the constant term to the right: Add '26.66666667' to each side of the equation. -26.66666667 + 3.111111111x + 26.66666667 + x2 = 0 + 26.66666667 Reorder the terms: -26.66666667 + 26.66666667 + 3.111111111x + x2 = 0 + 26.66666667 Combine like terms: -26.66666667 + 26.66666667 = 0.00000000 0.00000000 + 3.111111111x + x2 = 0 + 26.66666667 3.111111111x + x2 = 0 + 26.66666667 Combine like terms: 0 + 26.66666667 = 26.66666667 3.111111111x + x2 = 26.66666667 The x term is 3.111111111x. Take half its coefficient (1.555555556). Square it (2.419753088) and add it to both sides. Add '2.419753088' to each side of the equation. 3.111111111x + 2.419753088 + x2 = 26.66666667 + 2.419753088 Reorder the terms: 2.419753088 + 3.111111111x + x2 = 26.66666667 + 2.419753088 Combine like terms: 26.66666667 + 2.419753088 = 29.086419758 2.419753088 + 3.111111111x + x2 = 29.086419758 Factor a perfect square on the left side: (x + 1.555555556)(x + 1.555555556) = 29.086419758 Calculate the square root of the right side: 5.393182711 Break this problem into two subproblems by setting (x + 1.555555556) equal to 5.393182711 and -5.393182711.Subproblem 1
x + 1.555555556 = 5.393182711 Simplifying x + 1.555555556 = 5.393182711 Reorder the terms: 1.555555556 + x = 5.393182711 Solving 1.555555556 + x = 5.393182711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.555555556' to each side of the equation. 1.555555556 + -1.555555556 + x = 5.393182711 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + x = 5.393182711 + -1.555555556 x = 5.393182711 + -1.555555556 Combine like terms: 5.393182711 + -1.555555556 = 3.837627155 x = 3.837627155 Simplifying x = 3.837627155Subproblem 2
x + 1.555555556 = -5.393182711 Simplifying x + 1.555555556 = -5.393182711 Reorder the terms: 1.555555556 + x = -5.393182711 Solving 1.555555556 + x = -5.393182711 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.555555556' to each side of the equation. 1.555555556 + -1.555555556 + x = -5.393182711 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + x = -5.393182711 + -1.555555556 x = -5.393182711 + -1.555555556 Combine like terms: -5.393182711 + -1.555555556 = -6.948738267 x = -6.948738267 Simplifying x = -6.948738267Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.837627155, -6.948738267}
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