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Simplifying 6x + 16 + -9x2 + 7x + -9 = 0 Reorder the terms: 16 + -9 + 6x + 7x + -9x2 = 0 Combine like terms: 16 + -9 = 7 7 + 6x + 7x + -9x2 = 0 Combine like terms: 6x + 7x = 13x 7 + 13x + -9x2 = 0 Solving 7 + 13x + -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 + -1.444444444x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + -1.444444444x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + -1.444444444x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + -1.444444444x + x2 = 0 + 0.7777777778 -1.444444444x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 -1.444444444x + x2 = 0.7777777778 The x term is -1.444444444x. Take half its coefficient (-0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. -1.444444444x + 0.5216049380 + x2 = 0.7777777778 + 0.5216049380 Reorder the terms: 0.5216049380 + -1.444444444x + x2 = 0.7777777778 + 0.5216049380 Combine like terms: 0.7777777778 + 0.5216049380 = 1.2993827158 0.5216049380 + -1.444444444x + x2 = 1.2993827158 Factor a perfect square on the left side: (x + -0.722222222)(x + -0.722222222) = 1.2993827158 Calculate the square root of the right side: 1.139904696 Break this problem into two subproblems by setting (x + -0.722222222) equal to 1.139904696 and -1.139904696.Subproblem 1
x + -0.722222222 = 1.139904696 Simplifying x + -0.722222222 = 1.139904696 Reorder the terms: -0.722222222 + x = 1.139904696 Solving -0.722222222 + x = 1.139904696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = 1.139904696 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = 1.139904696 + 0.722222222 x = 1.139904696 + 0.722222222 Combine like terms: 1.139904696 + 0.722222222 = 1.862126918 x = 1.862126918 Simplifying x = 1.862126918Subproblem 2
x + -0.722222222 = -1.139904696 Simplifying x + -0.722222222 = -1.139904696 Reorder the terms: -0.722222222 + x = -1.139904696 Solving -0.722222222 + x = -1.139904696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.722222222' to each side of the equation. -0.722222222 + 0.722222222 + x = -1.139904696 + 0.722222222 Combine like terms: -0.722222222 + 0.722222222 = 0.000000000 0.000000000 + x = -1.139904696 + 0.722222222 x = -1.139904696 + 0.722222222 Combine like terms: -1.139904696 + 0.722222222 = -0.417682474 x = -0.417682474 Simplifying x = -0.417682474Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.862126918, -0.417682474}
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