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Simplifying 9x2 + -54x = 13 Reorder the terms: -54x + 9x2 = 13 Solving -54x + 9x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + -54x + 9x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -54x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.444444444 + -6x + x2 = 0 Move the constant term to the right: Add '1.444444444' to each side of the equation. -1.444444444 + -6x + 1.444444444 + x2 = 0 + 1.444444444 Reorder the terms: -1.444444444 + 1.444444444 + -6x + x2 = 0 + 1.444444444 Combine like terms: -1.444444444 + 1.444444444 = 0.000000000 0.000000000 + -6x + x2 = 0 + 1.444444444 -6x + x2 = 0 + 1.444444444 Combine like terms: 0 + 1.444444444 = 1.444444444 -6x + x2 = 1.444444444 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 1.444444444 + 9 Reorder the terms: 9 + -6x + x2 = 1.444444444 + 9 Combine like terms: 1.444444444 + 9 = 10.444444444 9 + -6x + x2 = 10.444444444 Factor a perfect square on the left side: (x + -3)(x + -3) = 10.444444444 Calculate the square root of the right side: 3.231786572 Break this problem into two subproblems by setting (x + -3) equal to 3.231786572 and -3.231786572.Subproblem 1
x + -3 = 3.231786572 Simplifying x + -3 = 3.231786572 Reorder the terms: -3 + x = 3.231786572 Solving -3 + x = 3.231786572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.231786572 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.231786572 + 3 x = 3.231786572 + 3 Combine like terms: 3.231786572 + 3 = 6.231786572 x = 6.231786572 Simplifying x = 6.231786572Subproblem 2
x + -3 = -3.231786572 Simplifying x + -3 = -3.231786572 Reorder the terms: -3 + x = -3.231786572 Solving -3 + x = -3.231786572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.231786572 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.231786572 + 3 x = -3.231786572 + 3 Combine like terms: -3.231786572 + 3 = -0.231786572 x = -0.231786572 Simplifying x = -0.231786572Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.231786572, -0.231786572}
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