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Simplifying 7x2 + -101x + -364 = 0 Reorder the terms: -364 + -101x + 7x2 = 0 Solving -364 + -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'. -52 + -14.42857143x + x2 = 0 Move the constant term to the right: Add '52' to each side of the equation. -52 + -14.42857143x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + -14.42857143x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -14.42857143x + x2 = 0 + 52 -14.42857143x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 -14.42857143x + x2 = 52 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 = 52 + 52.04591838 Reorder the terms: 52.04591838 + -14.42857143x + x2 = 52 + 52.04591838 Combine like terms: 52 + 52.04591838 = 104.04591838 52.04591838 + -14.42857143x + x2 = 104.04591838 Factor a perfect square on the left side: (x + -7.214285715)(x + -7.214285715) = 104.04591838 Calculate the square root of the right side: 10.200290113 Break this problem into two subproblems by setting (x + -7.214285715) equal to 10.200290113 and -10.200290113.Subproblem 1
x + -7.214285715 = 10.200290113 Simplifying x + -7.214285715 = 10.200290113 Reorder the terms: -7.214285715 + x = 10.200290113 Solving -7.214285715 + x = 10.200290113 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 = 10.200290113 + 7.214285715 Combine like terms: -7.214285715 + 7.214285715 = 0.000000000 0.000000000 + x = 10.200290113 + 7.214285715 x = 10.200290113 + 7.214285715 Combine like terms: 10.200290113 + 7.214285715 = 17.414575828 x = 17.414575828 Simplifying x = 17.414575828Subproblem 2
x + -7.214285715 = -10.200290113 Simplifying x + -7.214285715 = -10.200290113 Reorder the terms: -7.214285715 + x = -10.200290113 Solving -7.214285715 + x = -10.200290113 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 = -10.200290113 + 7.214285715 Combine like terms: -7.214285715 + 7.214285715 = 0.000000000 0.000000000 + x = -10.200290113 + 7.214285715 x = -10.200290113 + 7.214285715 Combine like terms: -10.200290113 + 7.214285715 = -2.986004398 x = -2.986004398 Simplifying x = -2.986004398Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.414575828, -2.986004398}
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