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Simplifying 9x2 + -54x + -70 = 0 Reorder the terms: -70 + -54x + 9x2 = 0 Solving -70 + -54x + 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'. -7.777777778 + -6x + x2 = 0 Move the constant term to the right: Add '7.777777778' to each side of the equation. -7.777777778 + -6x + 7.777777778 + x2 = 0 + 7.777777778 Reorder the terms: -7.777777778 + 7.777777778 + -6x + x2 = 0 + 7.777777778 Combine like terms: -7.777777778 + 7.777777778 = 0.000000000 0.000000000 + -6x + x2 = 0 + 7.777777778 -6x + x2 = 0 + 7.777777778 Combine like terms: 0 + 7.777777778 = 7.777777778 -6x + x2 = 7.777777778 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 = 7.777777778 + 9 Reorder the terms: 9 + -6x + x2 = 7.777777778 + 9 Combine like terms: 7.777777778 + 9 = 16.777777778 9 + -6x + x2 = 16.777777778 Factor a perfect square on the left side: (x + -3)(x + -3) = 16.777777778 Calculate the square root of the right side: 4.096068576 Break this problem into two subproblems by setting (x + -3) equal to 4.096068576 and -4.096068576.Subproblem 1
x + -3 = 4.096068576 Simplifying x + -3 = 4.096068576 Reorder the terms: -3 + x = 4.096068576 Solving -3 + x = 4.096068576 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 = 4.096068576 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.096068576 + 3 x = 4.096068576 + 3 Combine like terms: 4.096068576 + 3 = 7.096068576 x = 7.096068576 Simplifying x = 7.096068576Subproblem 2
x + -3 = -4.096068576 Simplifying x + -3 = -4.096068576 Reorder the terms: -3 + x = -4.096068576 Solving -3 + x = -4.096068576 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 = -4.096068576 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.096068576 + 3 x = -4.096068576 + 3 Combine like terms: -4.096068576 + 3 = -1.096068576 x = -1.096068576 Simplifying x = -1.096068576Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.096068576, -1.096068576}
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