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Simplifying 7x2 + 66x + 40 = 0 Reorder the terms: 40 + 66x + 7x2 = 0 Solving 40 + 66x + 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'. 5.714285714 + 9.428571429x + x2 = 0 Move the constant term to the right: Add '-5.714285714' to each side of the equation. 5.714285714 + 9.428571429x + -5.714285714 + x2 = 0 + -5.714285714 Reorder the terms: 5.714285714 + -5.714285714 + 9.428571429x + x2 = 0 + -5.714285714 Combine like terms: 5.714285714 + -5.714285714 = 0.000000000 0.000000000 + 9.428571429x + x2 = 0 + -5.714285714 9.428571429x + x2 = 0 + -5.714285714 Combine like terms: 0 + -5.714285714 = -5.714285714 9.428571429x + x2 = -5.714285714 The x term is 9.428571429x. Take half its coefficient (4.714285715). Square it (22.22448980) and add it to both sides. Add '22.22448980' to each side of the equation. 9.428571429x + 22.22448980 + x2 = -5.714285714 + 22.22448980 Reorder the terms: 22.22448980 + 9.428571429x + x2 = -5.714285714 + 22.22448980 Combine like terms: -5.714285714 + 22.22448980 = 16.510204086 22.22448980 + 9.428571429x + x2 = 16.510204086 Factor a perfect square on the left side: (x + 4.714285715)(x + 4.714285715) = 16.510204086 Calculate the square root of the right side: 4.063275044 Break this problem into two subproblems by setting (x + 4.714285715) equal to 4.063275044 and -4.063275044.Subproblem 1
x + 4.714285715 = 4.063275044 Simplifying x + 4.714285715 = 4.063275044 Reorder the terms: 4.714285715 + x = 4.063275044 Solving 4.714285715 + x = 4.063275044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.714285715' to each side of the equation. 4.714285715 + -4.714285715 + x = 4.063275044 + -4.714285715 Combine like terms: 4.714285715 + -4.714285715 = 0.000000000 0.000000000 + x = 4.063275044 + -4.714285715 x = 4.063275044 + -4.714285715 Combine like terms: 4.063275044 + -4.714285715 = -0.651010671 x = -0.651010671 Simplifying x = -0.651010671Subproblem 2
x + 4.714285715 = -4.063275044 Simplifying x + 4.714285715 = -4.063275044 Reorder the terms: 4.714285715 + x = -4.063275044 Solving 4.714285715 + x = -4.063275044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.714285715' to each side of the equation. 4.714285715 + -4.714285715 + x = -4.063275044 + -4.714285715 Combine like terms: 4.714285715 + -4.714285715 = 0.000000000 0.000000000 + x = -4.063275044 + -4.714285715 x = -4.063275044 + -4.714285715 Combine like terms: -4.063275044 + -4.714285715 = -8.777560759 x = -8.777560759 Simplifying x = -8.777560759Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.651010671, -8.777560759}
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