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Simplifying 7x2 + -33x + 22 = 0 Reorder the terms: 22 + -33x + 7x2 = 0 Solving 22 + -33x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 3.142857143 + -4.714285714x + x2 = 0 Move the constant term to the right: Add '-3.142857143' to each side of the equation. 3.142857143 + -4.714285714x + -3.142857143 + x2 = 0 + -3.142857143 Reorder the terms: 3.142857143 + -3.142857143 + -4.714285714x + x2 = 0 + -3.142857143 Combine like terms: 3.142857143 + -3.142857143 = 0.000000000 0.000000000 + -4.714285714x + x2 = 0 + -3.142857143 -4.714285714x + x2 = 0 + -3.142857143 Combine like terms: 0 + -3.142857143 = -3.142857143 -4.714285714x + x2 = -3.142857143 The x term is -4.714285714x. Take half its coefficient (-2.357142857). Square it (5.556122448) and add it to both sides. Add '5.556122448' to each side of the equation. -4.714285714x + 5.556122448 + x2 = -3.142857143 + 5.556122448 Reorder the terms: 5.556122448 + -4.714285714x + x2 = -3.142857143 + 5.556122448 Combine like terms: -3.142857143 + 5.556122448 = 2.413265305 5.556122448 + -4.714285714x + x2 = 2.413265305 Factor a perfect square on the left side: (x + -2.357142857)(x + -2.357142857) = 2.413265305 Calculate the square root of the right side: 1.553468798 Break this problem into two subproblems by setting (x + -2.357142857) equal to 1.553468798 and -1.553468798.Subproblem 1
x + -2.357142857 = 1.553468798 Simplifying x + -2.357142857 = 1.553468798 Reorder the terms: -2.357142857 + x = 1.553468798 Solving -2.357142857 + x = 1.553468798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.357142857' to each side of the equation. -2.357142857 + 2.357142857 + x = 1.553468798 + 2.357142857 Combine like terms: -2.357142857 + 2.357142857 = 0.000000000 0.000000000 + x = 1.553468798 + 2.357142857 x = 1.553468798 + 2.357142857 Combine like terms: 1.553468798 + 2.357142857 = 3.910611655 x = 3.910611655 Simplifying x = 3.910611655Subproblem 2
x + -2.357142857 = -1.553468798 Simplifying x + -2.357142857 = -1.553468798 Reorder the terms: -2.357142857 + x = -1.553468798 Solving -2.357142857 + x = -1.553468798 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.357142857' to each side of the equation. -2.357142857 + 2.357142857 + x = -1.553468798 + 2.357142857 Combine like terms: -2.357142857 + 2.357142857 = 0.000000000 0.000000000 + x = -1.553468798 + 2.357142857 x = -1.553468798 + 2.357142857 Combine like terms: -1.553468798 + 2.357142857 = 0.803674059 x = 0.803674059 Simplifying x = 0.803674059Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.910611655, 0.803674059}
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