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Simplifying 7x2 + 126x + 144 = 0 Reorder the terms: 144 + 126x + 7x2 = 0 Solving 144 + 126x + 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'. 20.57142857 + 18x + x2 = 0 Move the constant term to the right: Add '-20.57142857' to each side of the equation. 20.57142857 + 18x + -20.57142857 + x2 = 0 + -20.57142857 Reorder the terms: 20.57142857 + -20.57142857 + 18x + x2 = 0 + -20.57142857 Combine like terms: 20.57142857 + -20.57142857 = 0.00000000 0.00000000 + 18x + x2 = 0 + -20.57142857 18x + x2 = 0 + -20.57142857 Combine like terms: 0 + -20.57142857 = -20.57142857 18x + x2 = -20.57142857 The x term is 18x. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18x + 81 + x2 = -20.57142857 + 81 Reorder the terms: 81 + 18x + x2 = -20.57142857 + 81 Combine like terms: -20.57142857 + 81 = 60.42857143 81 + 18x + x2 = 60.42857143 Factor a perfect square on the left side: (x + 9)(x + 9) = 60.42857143 Calculate the square root of the right side: 7.773581635 Break this problem into two subproblems by setting (x + 9) equal to 7.773581635 and -7.773581635.Subproblem 1
x + 9 = 7.773581635 Simplifying x + 9 = 7.773581635 Reorder the terms: 9 + x = 7.773581635 Solving 9 + x = 7.773581635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = 7.773581635 + -9 Combine like terms: 9 + -9 = 0 0 + x = 7.773581635 + -9 x = 7.773581635 + -9 Combine like terms: 7.773581635 + -9 = -1.226418365 x = -1.226418365 Simplifying x = -1.226418365Subproblem 2
x + 9 = -7.773581635 Simplifying x + 9 = -7.773581635 Reorder the terms: 9 + x = -7.773581635 Solving 9 + x = -7.773581635 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + x = -7.773581635 + -9 Combine like terms: 9 + -9 = 0 0 + x = -7.773581635 + -9 x = -7.773581635 + -9 Combine like terms: -7.773581635 + -9 = -16.773581635 x = -16.773581635 Simplifying x = -16.773581635Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.226418365, -16.773581635}
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