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Simplifying x = 9x2 + 15x + -276 Reorder the terms: x = -276 + 15x + 9x2 Solving x = -276 + 15x + 9x2 Solving for variable 'x'. Reorder the terms: 276 + x + -15x + -9x2 = -276 + 15x + 9x2 + 276 + -15x + -9x2 Combine like terms: x + -15x = -14x 276 + -14x + -9x2 = -276 + 15x + 9x2 + 276 + -15x + -9x2 Reorder the terms: 276 + -14x + -9x2 = -276 + 276 + 15x + -15x + 9x2 + -9x2 Combine like terms: -276 + 276 = 0 276 + -14x + -9x2 = 0 + 15x + -15x + 9x2 + -9x2 276 + -14x + -9x2 = 15x + -15x + 9x2 + -9x2 Combine like terms: 15x + -15x = 0 276 + -14x + -9x2 = 0 + 9x2 + -9x2 276 + -14x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 276 + -14x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -30.66666667 + 1.555555556x + x2 = 0 Move the constant term to the right: Add '30.66666667' to each side of the equation. -30.66666667 + 1.555555556x + 30.66666667 + x2 = 0 + 30.66666667 Reorder the terms: -30.66666667 + 30.66666667 + 1.555555556x + x2 = 0 + 30.66666667 Combine like terms: -30.66666667 + 30.66666667 = 0.00000000 0.00000000 + 1.555555556x + x2 = 0 + 30.66666667 1.555555556x + x2 = 0 + 30.66666667 Combine like terms: 0 + 30.66666667 = 30.66666667 1.555555556x + x2 = 30.66666667 The x term is 1.555555556x. Take half its coefficient (0.777777778). Square it (0.6049382720) and add it to both sides. Add '0.6049382720' to each side of the equation. 1.555555556x + 0.6049382720 + x2 = 30.66666667 + 0.6049382720 Reorder the terms: 0.6049382720 + 1.555555556x + x2 = 30.66666667 + 0.6049382720 Combine like terms: 30.66666667 + 0.6049382720 = 31.271604942 0.6049382720 + 1.555555556x + x2 = 31.271604942 Factor a perfect square on the left side: (x + 0.777777778)(x + 0.777777778) = 31.271604942 Calculate the square root of the right side: 5.592102015 Break this problem into two subproblems by setting (x + 0.777777778) equal to 5.592102015 and -5.592102015.Subproblem 1
x + 0.777777778 = 5.592102015 Simplifying x + 0.777777778 = 5.592102015 Reorder the terms: 0.777777778 + x = 5.592102015 Solving 0.777777778 + x = 5.592102015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = 5.592102015 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = 5.592102015 + -0.777777778 x = 5.592102015 + -0.777777778 Combine like terms: 5.592102015 + -0.777777778 = 4.814324237 x = 4.814324237 Simplifying x = 4.814324237Subproblem 2
x + 0.777777778 = -5.592102015 Simplifying x + 0.777777778 = -5.592102015 Reorder the terms: 0.777777778 + x = -5.592102015 Solving 0.777777778 + x = -5.592102015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.777777778' to each side of the equation. 0.777777778 + -0.777777778 + x = -5.592102015 + -0.777777778 Combine like terms: 0.777777778 + -0.777777778 = 0.000000000 0.000000000 + x = -5.592102015 + -0.777777778 x = -5.592102015 + -0.777777778 Combine like terms: -5.592102015 + -0.777777778 = -6.369879793 x = -6.369879793 Simplifying x = -6.369879793Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.814324237, -6.369879793}
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