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Simplifying 7x2 + 76x = 8 Reorder the terms: 76x + 7x2 = 8 Solving 76x + 7x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 76x + 7x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 76x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + 10.85714286x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + 10.85714286x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + 10.85714286x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + 10.85714286x + x2 = 0 + 1.142857143 10.85714286x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 10.85714286x + x2 = 1.142857143 The x term is 10.85714286x. Take half its coefficient (5.42857143). Square it (29.46938777) and add it to both sides. Add '29.46938777' to each side of the equation. 10.85714286x + 29.46938777 + x2 = 1.142857143 + 29.46938777 Reorder the terms: 29.46938777 + 10.85714286x + x2 = 1.142857143 + 29.46938777 Combine like terms: 1.142857143 + 29.46938777 = 30.612244913 29.46938777 + 10.85714286x + x2 = 30.612244913 Factor a perfect square on the left side: (x + 5.42857143)(x + 5.42857143) = 30.612244913 Calculate the square root of the right side: 5.532833353 Break this problem into two subproblems by setting (x + 5.42857143) equal to 5.532833353 and -5.532833353.Subproblem 1
x + 5.42857143 = 5.532833353 Simplifying x + 5.42857143 = 5.532833353 Reorder the terms: 5.42857143 + x = 5.532833353 Solving 5.42857143 + x = 5.532833353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.42857143' to each side of the equation. 5.42857143 + -5.42857143 + x = 5.532833353 + -5.42857143 Combine like terms: 5.42857143 + -5.42857143 = 0.00000000 0.00000000 + x = 5.532833353 + -5.42857143 x = 5.532833353 + -5.42857143 Combine like terms: 5.532833353 + -5.42857143 = 0.104261923 x = 0.104261923 Simplifying x = 0.104261923Subproblem 2
x + 5.42857143 = -5.532833353 Simplifying x + 5.42857143 = -5.532833353 Reorder the terms: 5.42857143 + x = -5.532833353 Solving 5.42857143 + x = -5.532833353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.42857143' to each side of the equation. 5.42857143 + -5.42857143 + x = -5.532833353 + -5.42857143 Combine like terms: 5.42857143 + -5.42857143 = 0.00000000 0.00000000 + x = -5.532833353 + -5.42857143 x = -5.532833353 + -5.42857143 Combine like terms: -5.532833353 + -5.42857143 = -10.961404783 x = -10.961404783 Simplifying x = -10.961404783Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.104261923, -10.961404783}
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