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Simplifying 5x + -3 = 9x2 + -24 + 16 Reorder the terms: -3 + 5x = 9x2 + -24 + 16 Reorder the terms: -3 + 5x = -24 + 16 + 9x2 Combine like terms: -24 + 16 = -8 -3 + 5x = -8 + 9x2 Solving -3 + 5x = -8 + 9x2 Solving for variable 'x'. Reorder the terms: -3 + 8 + 5x + -9x2 = -8 + 9x2 + 8 + -9x2 Combine like terms: -3 + 8 = 5 5 + 5x + -9x2 = -8 + 9x2 + 8 + -9x2 Reorder the terms: 5 + 5x + -9x2 = -8 + 8 + 9x2 + -9x2 Combine like terms: -8 + 8 = 0 5 + 5x + -9x2 = 0 + 9x2 + -9x2 5 + 5x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 5 + 5x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.5555555556 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -0.5555555556x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -0.5555555556x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -0.5555555556x + x2 = 0 + 0.5555555556 -0.5555555556x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -0.5555555556x + x2 = 0.5555555556 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 = 0.5555555556 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 0.5555555556 + 0.07716049384 Combine like terms: 0.5555555556 + 0.07716049384 = 0.63271604944 0.07716049384 + -0.5555555556x + x2 = 0.63271604944 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 0.63271604944 Calculate the square root of the right side: 0.795434504 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 0.795434504 and -0.795434504.Subproblem 1
x + -0.2777777778 = 0.795434504 Simplifying x + -0.2777777778 = 0.795434504 Reorder the terms: -0.2777777778 + x = 0.795434504 Solving -0.2777777778 + x = 0.795434504 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 = 0.795434504 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 0.795434504 + 0.2777777778 x = 0.795434504 + 0.2777777778 Combine like terms: 0.795434504 + 0.2777777778 = 1.0732122818 x = 1.0732122818 Simplifying x = 1.0732122818Subproblem 2
x + -0.2777777778 = -0.795434504 Simplifying x + -0.2777777778 = -0.795434504 Reorder the terms: -0.2777777778 + x = -0.795434504 Solving -0.2777777778 + x = -0.795434504 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 = -0.795434504 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -0.795434504 + 0.2777777778 x = -0.795434504 + 0.2777777778 Combine like terms: -0.795434504 + 0.2777777778 = -0.5176567262 x = -0.5176567262 Simplifying x = -0.5176567262Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0732122818, -0.5176567262}
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