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Simplifying 9x2 + -18x + -56 = 0 Reorder the terms: -56 + -18x + 9x2 = 0 Solving -56 + -18x + 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'. -6.222222222 + -2x + x2 = 0 Move the constant term to the right: Add '6.222222222' to each side of the equation. -6.222222222 + -2x + 6.222222222 + x2 = 0 + 6.222222222 Reorder the terms: -6.222222222 + 6.222222222 + -2x + x2 = 0 + 6.222222222 Combine like terms: -6.222222222 + 6.222222222 = 0.000000000 0.000000000 + -2x + x2 = 0 + 6.222222222 -2x + x2 = 0 + 6.222222222 Combine like terms: 0 + 6.222222222 = 6.222222222 -2x + x2 = 6.222222222 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 6.222222222 + 1 Reorder the terms: 1 + -2x + x2 = 6.222222222 + 1 Combine like terms: 6.222222222 + 1 = 7.222222222 1 + -2x + x2 = 7.222222222 Factor a perfect square on the left side: (x + -1)(x + -1) = 7.222222222 Calculate the square root of the right side: 2.687419249 Break this problem into two subproblems by setting (x + -1) equal to 2.687419249 and -2.687419249.Subproblem 1
x + -1 = 2.687419249 Simplifying x + -1 = 2.687419249 Reorder the terms: -1 + x = 2.687419249 Solving -1 + x = 2.687419249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.687419249 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.687419249 + 1 x = 2.687419249 + 1 Combine like terms: 2.687419249 + 1 = 3.687419249 x = 3.687419249 Simplifying x = 3.687419249Subproblem 2
x + -1 = -2.687419249 Simplifying x + -1 = -2.687419249 Reorder the terms: -1 + x = -2.687419249 Solving -1 + x = -2.687419249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.687419249 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.687419249 + 1 x = -2.687419249 + 1 Combine like terms: -2.687419249 + 1 = -1.687419249 x = -1.687419249 Simplifying x = -1.687419249Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.687419249, -1.687419249}
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