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Simplifying 9x2 + -54x + 8 = 12 Reorder the terms: 8 + -54x + 9x2 = 12 Solving 8 + -54x + 9x2 = 12 Solving for variable 'x'. Reorder the terms: 8 + -12 + -54x + 9x2 = 12 + -12 Combine like terms: 8 + -12 = -4 -4 + -54x + 9x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -4 + -54x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + -6x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -6x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -6x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -6x + x2 = 0 + 0.4444444444 -6x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -6x + x2 = 0.4444444444 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 = 0.4444444444 + 9 Reorder the terms: 9 + -6x + x2 = 0.4444444444 + 9 Combine like terms: 0.4444444444 + 9 = 9.4444444444 9 + -6x + x2 = 9.4444444444 Factor a perfect square on the left side: (x + -3)(x + -3) = 9.4444444444 Calculate the square root of the right side: 3.073181486 Break this problem into two subproblems by setting (x + -3) equal to 3.073181486 and -3.073181486.Subproblem 1
x + -3 = 3.073181486 Simplifying x + -3 = 3.073181486 Reorder the terms: -3 + x = 3.073181486 Solving -3 + x = 3.073181486 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 = 3.073181486 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.073181486 + 3 x = 3.073181486 + 3 Combine like terms: 3.073181486 + 3 = 6.073181486 x = 6.073181486 Simplifying x = 6.073181486Subproblem 2
x + -3 = -3.073181486 Simplifying x + -3 = -3.073181486 Reorder the terms: -3 + x = -3.073181486 Solving -3 + x = -3.073181486 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 = -3.073181486 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.073181486 + 3 x = -3.073181486 + 3 Combine like terms: -3.073181486 + 3 = -0.073181486 x = -0.073181486 Simplifying x = -0.073181486Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.073181486, -0.073181486}
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