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Simplifying 7x2 + 141x + -108 = 0 Reorder the terms: -108 + 141x + 7x2 = 0 Solving -108 + 141x + 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'. -15.42857143 + 20.14285714x + x2 = 0 Move the constant term to the right: Add '15.42857143' to each side of the equation. -15.42857143 + 20.14285714x + 15.42857143 + x2 = 0 + 15.42857143 Reorder the terms: -15.42857143 + 15.42857143 + 20.14285714x + x2 = 0 + 15.42857143 Combine like terms: -15.42857143 + 15.42857143 = 0.00000000 0.00000000 + 20.14285714x + x2 = 0 + 15.42857143 20.14285714x + x2 = 0 + 15.42857143 Combine like terms: 0 + 15.42857143 = 15.42857143 20.14285714x + x2 = 15.42857143 The x term is 20.14285714x. Take half its coefficient (10.07142857). Square it (101.4336734) and add it to both sides. Add '101.4336734' to each side of the equation. 20.14285714x + 101.4336734 + x2 = 15.42857143 + 101.4336734 Reorder the terms: 101.4336734 + 20.14285714x + x2 = 15.42857143 + 101.4336734 Combine like terms: 15.42857143 + 101.4336734 = 116.86224483 101.4336734 + 20.14285714x + x2 = 116.86224483 Factor a perfect square on the left side: (x + 10.07142857)(x + 10.07142857) = 116.86224483 Calculate the square root of the right side: 10.810284216 Break this problem into two subproblems by setting (x + 10.07142857) equal to 10.810284216 and -10.810284216.Subproblem 1
x + 10.07142857 = 10.810284216 Simplifying x + 10.07142857 = 10.810284216 Reorder the terms: 10.07142857 + x = 10.810284216 Solving 10.07142857 + x = 10.810284216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.07142857' to each side of the equation. 10.07142857 + -10.07142857 + x = 10.810284216 + -10.07142857 Combine like terms: 10.07142857 + -10.07142857 = 0.00000000 0.00000000 + x = 10.810284216 + -10.07142857 x = 10.810284216 + -10.07142857 Combine like terms: 10.810284216 + -10.07142857 = 0.738855646 x = 0.738855646 Simplifying x = 0.738855646Subproblem 2
x + 10.07142857 = -10.810284216 Simplifying x + 10.07142857 = -10.810284216 Reorder the terms: 10.07142857 + x = -10.810284216 Solving 10.07142857 + x = -10.810284216 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.07142857' to each side of the equation. 10.07142857 + -10.07142857 + x = -10.810284216 + -10.07142857 Combine like terms: 10.07142857 + -10.07142857 = 0.00000000 0.00000000 + x = -10.810284216 + -10.07142857 x = -10.810284216 + -10.07142857 Combine like terms: -10.810284216 + -10.07142857 = -20.881712786 x = -20.881712786 Simplifying x = -20.881712786Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.738855646, -20.881712786}
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