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Simplifying x(9x + -5) = 45 Reorder the terms: x(-5 + 9x) = 45 (-5 * x + 9x * x) = 45 (-5x + 9x2) = 45 Solving -5x + 9x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -5x + 9x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -5 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -0.5555555556x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -0.5555555556x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -0.5555555556x + x2 = 0 + 5 -0.5555555556x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -0.5555555556x + x2 = 5 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 = 5 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 5 + 0.07716049384 Combine like terms: 5 + 0.07716049384 = 5.07716049384 0.07716049384 + -0.5555555556x + x2 = 5.07716049384 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 5.07716049384 Calculate the square root of the right side: 2.253255532 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 2.253255532 and -2.253255532.Subproblem 1
x + -0.2777777778 = 2.253255532 Simplifying x + -0.2777777778 = 2.253255532 Reorder the terms: -0.2777777778 + x = 2.253255532 Solving -0.2777777778 + x = 2.253255532 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 = 2.253255532 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 2.253255532 + 0.2777777778 x = 2.253255532 + 0.2777777778 Combine like terms: 2.253255532 + 0.2777777778 = 2.5310333098 x = 2.5310333098 Simplifying x = 2.5310333098Subproblem 2
x + -0.2777777778 = -2.253255532 Simplifying x + -0.2777777778 = -2.253255532 Reorder the terms: -0.2777777778 + x = -2.253255532 Solving -0.2777777778 + x = -2.253255532 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 = -2.253255532 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -2.253255532 + 0.2777777778 x = -2.253255532 + 0.2777777778 Combine like terms: -2.253255532 + 0.2777777778 = -1.9754777542 x = -1.9754777542 Simplifying x = -1.9754777542Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5310333098, -1.9754777542}
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