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Simplifying 9x2 + -113x + 306 = 0 Reorder the terms: 306 + -113x + 9x2 = 0 Solving 306 + -113x + 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'. 34 + -12.55555556x + x2 = 0 Move the constant term to the right: Add '-34' to each side of the equation. 34 + -12.55555556x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + -12.55555556x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -12.55555556x + x2 = 0 + -34 -12.55555556x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 -12.55555556x + x2 = -34 The x term is -12.55555556x. Take half its coefficient (-6.27777778). Square it (39.41049386) and add it to both sides. Add '39.41049386' to each side of the equation. -12.55555556x + 39.41049386 + x2 = -34 + 39.41049386 Reorder the terms: 39.41049386 + -12.55555556x + x2 = -34 + 39.41049386 Combine like terms: -34 + 39.41049386 = 5.41049386 39.41049386 + -12.55555556x + x2 = 5.41049386 Factor a perfect square on the left side: (x + -6.27777778)(x + -6.27777778) = 5.41049386 Calculate the square root of the right side: 2.326046831 Break this problem into two subproblems by setting (x + -6.27777778) equal to 2.326046831 and -2.326046831.Subproblem 1
x + -6.27777778 = 2.326046831 Simplifying x + -6.27777778 = 2.326046831 Reorder the terms: -6.27777778 + x = 2.326046831 Solving -6.27777778 + x = 2.326046831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.27777778' to each side of the equation. -6.27777778 + 6.27777778 + x = 2.326046831 + 6.27777778 Combine like terms: -6.27777778 + 6.27777778 = 0.00000000 0.00000000 + x = 2.326046831 + 6.27777778 x = 2.326046831 + 6.27777778 Combine like terms: 2.326046831 + 6.27777778 = 8.603824611 x = 8.603824611 Simplifying x = 8.603824611Subproblem 2
x + -6.27777778 = -2.326046831 Simplifying x + -6.27777778 = -2.326046831 Reorder the terms: -6.27777778 + x = -2.326046831 Solving -6.27777778 + x = -2.326046831 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.27777778' to each side of the equation. -6.27777778 + 6.27777778 + x = -2.326046831 + 6.27777778 Combine like terms: -6.27777778 + 6.27777778 = 0.00000000 0.00000000 + x = -2.326046831 + 6.27777778 x = -2.326046831 + 6.27777778 Combine like terms: -2.326046831 + 6.27777778 = 3.951730949 x = 3.951730949 Simplifying x = 3.951730949Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.603824611, 3.951730949}
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