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Simplifying 9x2 + 4x + -60 = 0 Reorder the terms: -60 + 4x + 9x2 = 0 Solving -60 + 4x + 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'. -6.666666667 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + 0.4444444444x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + 0.4444444444x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + 0.4444444444x + x2 = 0 + 6.666666667 0.4444444444x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 0.4444444444x + x2 = 6.666666667 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 6.666666667 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 6.666666667 + 0.04938271604 Combine like terms: 6.666666667 + 0.04938271604 = 6.71604938304 0.04938271604 + 0.4444444444x + x2 = 6.71604938304 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 6.71604938304 Calculate the square root of the right side: 2.591534176 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 2.591534176 and -2.591534176.Subproblem 1
x + 0.2222222222 = 2.591534176 Simplifying x + 0.2222222222 = 2.591534176 Reorder the terms: 0.2222222222 + x = 2.591534176 Solving 0.2222222222 + x = 2.591534176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 2.591534176 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 2.591534176 + -0.2222222222 x = 2.591534176 + -0.2222222222 Combine like terms: 2.591534176 + -0.2222222222 = 2.3693119538 x = 2.3693119538 Simplifying x = 2.3693119538Subproblem 2
x + 0.2222222222 = -2.591534176 Simplifying x + 0.2222222222 = -2.591534176 Reorder the terms: 0.2222222222 + x = -2.591534176 Solving 0.2222222222 + x = -2.591534176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -2.591534176 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -2.591534176 + -0.2222222222 x = -2.591534176 + -0.2222222222 Combine like terms: -2.591534176 + -0.2222222222 = -2.8137563982 x = -2.8137563982 Simplifying x = -2.8137563982Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3693119538, -2.8137563982}
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