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Simplifying 9x2 + -14x + -208 = 0 Reorder the terms: -208 + -14x + 9x2 = 0 Solving -208 + -14x + 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'. -23.11111111 + -1.555555556x + x2 = 0 Move the constant term to the right: Add '23.11111111' to each side of the equation. -23.11111111 + -1.555555556x + 23.11111111 + x2 = 0 + 23.11111111 Reorder the terms: -23.11111111 + 23.11111111 + -1.555555556x + x2 = 0 + 23.11111111 Combine like terms: -23.11111111 + 23.11111111 = 0.00000000 0.00000000 + -1.555555556x + x2 = 0 + 23.11111111 -1.555555556x + x2 = 0 + 23.11111111 Combine like terms: 0 + 23.11111111 = 23.11111111 -1.555555556x + x2 = 23.11111111 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 = 23.11111111 + 0.6049382720 Reorder the terms: 0.6049382720 + -1.555555556x + x2 = 23.11111111 + 0.6049382720 Combine like terms: 23.11111111 + 0.6049382720 = 23.716049382 0.6049382720 + -1.555555556x + x2 = 23.716049382 Factor a perfect square on the left side: (x + -0.777777778)(x + -0.777777778) = 23.716049382 Calculate the square root of the right side: 4.869912667 Break this problem into two subproblems by setting (x + -0.777777778) equal to 4.869912667 and -4.869912667.Subproblem 1
x + -0.777777778 = 4.869912667 Simplifying x + -0.777777778 = 4.869912667 Reorder the terms: -0.777777778 + x = 4.869912667 Solving -0.777777778 + x = 4.869912667 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 = 4.869912667 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = 4.869912667 + 0.777777778 x = 4.869912667 + 0.777777778 Combine like terms: 4.869912667 + 0.777777778 = 5.647690445 x = 5.647690445 Simplifying x = 5.647690445Subproblem 2
x + -0.777777778 = -4.869912667 Simplifying x + -0.777777778 = -4.869912667 Reorder the terms: -0.777777778 + x = -4.869912667 Solving -0.777777778 + x = -4.869912667 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 = -4.869912667 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = -4.869912667 + 0.777777778 x = -4.869912667 + 0.777777778 Combine like terms: -4.869912667 + 0.777777778 = -4.092134889 x = -4.092134889 Simplifying x = -4.092134889Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.647690445, -4.092134889}
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