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Simplifying 9x2 + 18x + 9 + 20(x + 1) + -7 = 0 Reorder the terms: 9x2 + 18x + 9 + 20(1 + x) + -7 = 0 9x2 + 18x + 9 + (1 * 20 + x * 20) + -7 = 0 9x2 + 18x + 9 + (20 + 20x) + -7 = 0 Reorder the terms: 9 + 20 + -7 + 18x + 20x + 9x2 = 0 Combine like terms: 9 + 20 = 29 29 + -7 + 18x + 20x + 9x2 = 0 Combine like terms: 29 + -7 = 22 22 + 18x + 20x + 9x2 = 0 Combine like terms: 18x + 20x = 38x 22 + 38x + 9x2 = 0 Solving 22 + 38x + 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'. 2.444444444 + 4.222222222x + x2 = 0 Move the constant term to the right: Add '-2.444444444' to each side of the equation. 2.444444444 + 4.222222222x + -2.444444444 + x2 = 0 + -2.444444444 Reorder the terms: 2.444444444 + -2.444444444 + 4.222222222x + x2 = 0 + -2.444444444 Combine like terms: 2.444444444 + -2.444444444 = 0.000000000 0.000000000 + 4.222222222x + x2 = 0 + -2.444444444 4.222222222x + x2 = 0 + -2.444444444 Combine like terms: 0 + -2.444444444 = -2.444444444 4.222222222x + x2 = -2.444444444 The x term is 4.222222222x. Take half its coefficient (2.111111111). Square it (4.456790123) and add it to both sides. Add '4.456790123' to each side of the equation. 4.222222222x + 4.456790123 + x2 = -2.444444444 + 4.456790123 Reorder the terms: 4.456790123 + 4.222222222x + x2 = -2.444444444 + 4.456790123 Combine like terms: -2.444444444 + 4.456790123 = 2.012345679 4.456790123 + 4.222222222x + x2 = 2.012345679 Factor a perfect square on the left side: (x + 2.111111111)(x + 2.111111111) = 2.012345679 Calculate the square root of the right side: 1.418571704 Break this problem into two subproblems by setting (x + 2.111111111) equal to 1.418571704 and -1.418571704.Subproblem 1
x + 2.111111111 = 1.418571704 Simplifying x + 2.111111111 = 1.418571704 Reorder the terms: 2.111111111 + x = 1.418571704 Solving 2.111111111 + x = 1.418571704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.111111111' to each side of the equation. 2.111111111 + -2.111111111 + x = 1.418571704 + -2.111111111 Combine like terms: 2.111111111 + -2.111111111 = 0.000000000 0.000000000 + x = 1.418571704 + -2.111111111 x = 1.418571704 + -2.111111111 Combine like terms: 1.418571704 + -2.111111111 = -0.692539407 x = -0.692539407 Simplifying x = -0.692539407Subproblem 2
x + 2.111111111 = -1.418571704 Simplifying x + 2.111111111 = -1.418571704 Reorder the terms: 2.111111111 + x = -1.418571704 Solving 2.111111111 + x = -1.418571704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.111111111' to each side of the equation. 2.111111111 + -2.111111111 + x = -1.418571704 + -2.111111111 Combine like terms: 2.111111111 + -2.111111111 = 0.000000000 0.000000000 + x = -1.418571704 + -2.111111111 x = -1.418571704 + -2.111111111 Combine like terms: -1.418571704 + -2.111111111 = -3.529682815 x = -3.529682815 Simplifying x = -3.529682815Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.692539407, -3.529682815}
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