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Simplifying 9x2 + -149x + 510 = 0 Reorder the terms: 510 + -149x + 9x2 = 0 Solving 510 + -149x + 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'. 56.66666667 + -16.55555556x + x2 = 0 Move the constant term to the right: Add '-56.66666667' to each side of the equation. 56.66666667 + -16.55555556x + -56.66666667 + x2 = 0 + -56.66666667 Reorder the terms: 56.66666667 + -56.66666667 + -16.55555556x + x2 = 0 + -56.66666667 Combine like terms: 56.66666667 + -56.66666667 = 0.00000000 0.00000000 + -16.55555556x + x2 = 0 + -56.66666667 -16.55555556x + x2 = 0 + -56.66666667 Combine like terms: 0 + -56.66666667 = -56.66666667 -16.55555556x + x2 = -56.66666667 The x term is -16.55555556x. Take half its coefficient (-8.27777778). Square it (68.52160498) and add it to both sides. Add '68.52160498' to each side of the equation. -16.55555556x + 68.52160498 + x2 = -56.66666667 + 68.52160498 Reorder the terms: 68.52160498 + -16.55555556x + x2 = -56.66666667 + 68.52160498 Combine like terms: -56.66666667 + 68.52160498 = 11.85493831 68.52160498 + -16.55555556x + x2 = 11.85493831 Factor a perfect square on the left side: (x + -8.27777778)(x + -8.27777778) = 11.85493831 Calculate the square root of the right side: 3.443100102 Break this problem into two subproblems by setting (x + -8.27777778) equal to 3.443100102 and -3.443100102.Subproblem 1
x + -8.27777778 = 3.443100102 Simplifying x + -8.27777778 = 3.443100102 Reorder the terms: -8.27777778 + x = 3.443100102 Solving -8.27777778 + x = 3.443100102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.27777778' to each side of the equation. -8.27777778 + 8.27777778 + x = 3.443100102 + 8.27777778 Combine like terms: -8.27777778 + 8.27777778 = 0.00000000 0.00000000 + x = 3.443100102 + 8.27777778 x = 3.443100102 + 8.27777778 Combine like terms: 3.443100102 + 8.27777778 = 11.720877882 x = 11.720877882 Simplifying x = 11.720877882Subproblem 2
x + -8.27777778 = -3.443100102 Simplifying x + -8.27777778 = -3.443100102 Reorder the terms: -8.27777778 + x = -3.443100102 Solving -8.27777778 + x = -3.443100102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.27777778' to each side of the equation. -8.27777778 + 8.27777778 + x = -3.443100102 + 8.27777778 Combine like terms: -8.27777778 + 8.27777778 = 0.00000000 0.00000000 + x = -3.443100102 + 8.27777778 x = -3.443100102 + 8.27777778 Combine like terms: -3.443100102 + 8.27777778 = 4.834677678 x = 4.834677678 Simplifying x = 4.834677678Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.720877882, 4.834677678}
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