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Simplifying 9x2 + 20x + -45 = 0 Reorder the terms: -45 + 20x + 9x2 = 0 Solving -45 + 20x + 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'. -5 + 2.222222222x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2.222222222x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 2.222222222x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2.222222222x + x2 = 0 + 5 2.222222222x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 2.222222222x + x2 = 5 The x term is 2.222222222x. Take half its coefficient (1.111111111). Square it (1.234567901) and add it to both sides. Add '1.234567901' to each side of the equation. 2.222222222x + 1.234567901 + x2 = 5 + 1.234567901 Reorder the terms: 1.234567901 + 2.222222222x + x2 = 5 + 1.234567901 Combine like terms: 5 + 1.234567901 = 6.234567901 1.234567901 + 2.222222222x + x2 = 6.234567901 Factor a perfect square on the left side: (x + 1.111111111)(x + 1.111111111) = 6.234567901 Calculate the square root of the right side: 2.496911673 Break this problem into two subproblems by setting (x + 1.111111111) equal to 2.496911673 and -2.496911673.Subproblem 1
x + 1.111111111 = 2.496911673 Simplifying x + 1.111111111 = 2.496911673 Reorder the terms: 1.111111111 + x = 2.496911673 Solving 1.111111111 + x = 2.496911673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + x = 2.496911673 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + x = 2.496911673 + -1.111111111 x = 2.496911673 + -1.111111111 Combine like terms: 2.496911673 + -1.111111111 = 1.385800562 x = 1.385800562 Simplifying x = 1.385800562Subproblem 2
x + 1.111111111 = -2.496911673 Simplifying x + 1.111111111 = -2.496911673 Reorder the terms: 1.111111111 + x = -2.496911673 Solving 1.111111111 + x = -2.496911673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + x = -2.496911673 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + x = -2.496911673 + -1.111111111 x = -2.496911673 + -1.111111111 Combine like terms: -2.496911673 + -1.111111111 = -3.608022784 x = -3.608022784 Simplifying x = -3.608022784Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.385800562, -3.608022784}
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