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Simplifying 9x2 + -20x + -252 = 0 Reorder the terms: -252 + -20x + 9x2 = 0 Solving -252 + -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'. -28 + -2.222222222x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + -2.222222222x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -2.222222222x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -2.222222222x + x2 = 0 + 28 -2.222222222x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -2.222222222x + x2 = 28 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 = 28 + 1.234567901 Reorder the terms: 1.234567901 + -2.222222222x + x2 = 28 + 1.234567901 Combine like terms: 28 + 1.234567901 = 29.234567901 1.234567901 + -2.222222222x + x2 = 29.234567901 Factor a perfect square on the left side: (x + -1.111111111)(x + -1.111111111) = 29.234567901 Calculate the square root of the right side: 5.406900027 Break this problem into two subproblems by setting (x + -1.111111111) equal to 5.406900027 and -5.406900027.Subproblem 1
x + -1.111111111 = 5.406900027 Simplifying x + -1.111111111 = 5.406900027 Reorder the terms: -1.111111111 + x = 5.406900027 Solving -1.111111111 + x = 5.406900027 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 = 5.406900027 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = 5.406900027 + 1.111111111 x = 5.406900027 + 1.111111111 Combine like terms: 5.406900027 + 1.111111111 = 6.518011138 x = 6.518011138 Simplifying x = 6.518011138Subproblem 2
x + -1.111111111 = -5.406900027 Simplifying x + -1.111111111 = -5.406900027 Reorder the terms: -1.111111111 + x = -5.406900027 Solving -1.111111111 + x = -5.406900027 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 = -5.406900027 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + x = -5.406900027 + 1.111111111 x = -5.406900027 + 1.111111111 Combine like terms: -5.406900027 + 1.111111111 = -4.295788916 x = -4.295788916 Simplifying x = -4.295788916Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.518011138, -4.295788916}
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