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Simplifying 9x2 + 28x + 7 = 0 Reorder the terms: 7 + 28x + 9x2 = 0 Solving 7 + 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'. 0.7777777778 + 3.111111111x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + 3.111111111x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + 3.111111111x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + 3.111111111x + x2 = 0 + -0.7777777778 3.111111111x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 3.111111111x + x2 = -0.7777777778 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 = -0.7777777778 + 2.419753088 Reorder the terms: 2.419753088 + 3.111111111x + x2 = -0.7777777778 + 2.419753088 Combine like terms: -0.7777777778 + 2.419753088 = 1.6419753102 2.419753088 + 3.111111111x + x2 = 1.6419753102 Factor a perfect square on the left side: (x + 1.555555556)(x + 1.555555556) = 1.6419753102 Calculate the square root of the right side: 1.281395844 Break this problem into two subproblems by setting (x + 1.555555556) equal to 1.281395844 and -1.281395844.Subproblem 1
x + 1.555555556 = 1.281395844 Simplifying x + 1.555555556 = 1.281395844 Reorder the terms: 1.555555556 + x = 1.281395844 Solving 1.555555556 + x = 1.281395844 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 = 1.281395844 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + x = 1.281395844 + -1.555555556 x = 1.281395844 + -1.555555556 Combine like terms: 1.281395844 + -1.555555556 = -0.274159712 x = -0.274159712 Simplifying x = -0.274159712Subproblem 2
x + 1.555555556 = -1.281395844 Simplifying x + 1.555555556 = -1.281395844 Reorder the terms: 1.555555556 + x = -1.281395844 Solving 1.555555556 + x = -1.281395844 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 = -1.281395844 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + x = -1.281395844 + -1.555555556 x = -1.281395844 + -1.555555556 Combine like terms: -1.281395844 + -1.555555556 = -2.8369514 x = -2.8369514 Simplifying x = -2.8369514Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.274159712, -2.8369514}
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