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Simplifying 7x2 + -101x + 322 = 0 Reorder the terms: 322 + -101x + 7x2 = 0 Solving 322 + -101x + 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'. 46 + -14.42857143x + x2 = 0 Move the constant term to the right: Add '-46' to each side of the equation. 46 + -14.42857143x + -46 + x2 = 0 + -46 Reorder the terms: 46 + -46 + -14.42857143x + x2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + -14.42857143x + x2 = 0 + -46 -14.42857143x + x2 = 0 + -46 Combine like terms: 0 + -46 = -46 -14.42857143x + x2 = -46 The x term is -14.42857143x. Take half its coefficient (-7.214285715). Square it (52.04591838) and add it to both sides. Add '52.04591838' to each side of the equation. -14.42857143x + 52.04591838 + x2 = -46 + 52.04591838 Reorder the terms: 52.04591838 + -14.42857143x + x2 = -46 + 52.04591838 Combine like terms: -46 + 52.04591838 = 6.04591838 52.04591838 + -14.42857143x + x2 = 6.04591838 Factor a perfect square on the left side: (x + -7.214285715)(x + -7.214285715) = 6.04591838 Calculate the square root of the right side: 2.458844928 Break this problem into two subproblems by setting (x + -7.214285715) equal to 2.458844928 and -2.458844928.Subproblem 1
x + -7.214285715 = 2.458844928 Simplifying x + -7.214285715 = 2.458844928 Reorder the terms: -7.214285715 + x = 2.458844928 Solving -7.214285715 + x = 2.458844928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.214285715' to each side of the equation. -7.214285715 + 7.214285715 + x = 2.458844928 + 7.214285715 Combine like terms: -7.214285715 + 7.214285715 = 0.000000000 0.000000000 + x = 2.458844928 + 7.214285715 x = 2.458844928 + 7.214285715 Combine like terms: 2.458844928 + 7.214285715 = 9.673130643 x = 9.673130643 Simplifying x = 9.673130643Subproblem 2
x + -7.214285715 = -2.458844928 Simplifying x + -7.214285715 = -2.458844928 Reorder the terms: -7.214285715 + x = -2.458844928 Solving -7.214285715 + x = -2.458844928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.214285715' to each side of the equation. -7.214285715 + 7.214285715 + x = -2.458844928 + 7.214285715 Combine like terms: -7.214285715 + 7.214285715 = 0.000000000 0.000000000 + x = -2.458844928 + 7.214285715 x = -2.458844928 + 7.214285715 Combine like terms: -2.458844928 + 7.214285715 = 4.755440787 x = 4.755440787 Simplifying x = 4.755440787Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.673130643, 4.755440787}
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