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Simplifying 9x2 + -5x + -360 = 0 Reorder the terms: -360 + -5x + 9x2 = 0 Solving -360 + -5x + 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'. -40 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -0.5555555556x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -0.5555555556x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -0.5555555556x + x2 = 0 + 40 -0.5555555556x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -0.5555555556x + x2 = 40 The x term is -0.5555555556x. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556x + 0.07716049384 + x2 = 40 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 40 + 0.07716049384 Combine like terms: 40 + 0.07716049384 = 40.07716049384 0.07716049384 + -0.5555555556x + x2 = 40.07716049384 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 40.07716049384 Calculate the square root of the right side: 6.330652454 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 6.330652454 and -6.330652454.Subproblem 1
x + -0.2777777778 = 6.330652454 Simplifying x + -0.2777777778 = 6.330652454 Reorder the terms: -0.2777777778 + x = 6.330652454 Solving -0.2777777778 + x = 6.330652454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = 6.330652454 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 6.330652454 + 0.2777777778 x = 6.330652454 + 0.2777777778 Combine like terms: 6.330652454 + 0.2777777778 = 6.6084302318 x = 6.6084302318 Simplifying x = 6.6084302318Subproblem 2
x + -0.2777777778 = -6.330652454 Simplifying x + -0.2777777778 = -6.330652454 Reorder the terms: -0.2777777778 + x = -6.330652454 Solving -0.2777777778 + x = -6.330652454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = -6.330652454 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -6.330652454 + 0.2777777778 x = -6.330652454 + 0.2777777778 Combine like terms: -6.330652454 + 0.2777777778 = -6.0528746762 x = -6.0528746762 Simplifying x = -6.0528746762Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.6084302318, -6.0528746762}
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