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Simplifying 72x2 + 144x + 71 = 0 Reorder the terms: 71 + 144x + 72x2 = 0 Solving 71 + 144x + 72x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. 0.9861111111 + 2x + x2 = 0 Move the constant term to the right: Add '-0.9861111111' to each side of the equation. 0.9861111111 + 2x + -0.9861111111 + x2 = 0 + -0.9861111111 Reorder the terms: 0.9861111111 + -0.9861111111 + 2x + x2 = 0 + -0.9861111111 Combine like terms: 0.9861111111 + -0.9861111111 = 0.0000000000 0.0000000000 + 2x + x2 = 0 + -0.9861111111 2x + x2 = 0 + -0.9861111111 Combine like terms: 0 + -0.9861111111 = -0.9861111111 2x + x2 = -0.9861111111 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -0.9861111111 + 1 Reorder the terms: 1 + 2x + x2 = -0.9861111111 + 1 Combine like terms: -0.9861111111 + 1 = 0.0138888889 1 + 2x + x2 = 0.0138888889 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.0138888889 Calculate the square root of the right side: 0.11785113 Break this problem into two subproblems by setting (x + 1) equal to 0.11785113 and -0.11785113.Subproblem 1
x + 1 = 0.11785113 Simplifying x + 1 = 0.11785113 Reorder the terms: 1 + x = 0.11785113 Solving 1 + x = 0.11785113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 0.11785113 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.11785113 + -1 x = 0.11785113 + -1 Combine like terms: 0.11785113 + -1 = -0.88214887 x = -0.88214887 Simplifying x = -0.88214887Subproblem 2
x + 1 = -0.11785113 Simplifying x + 1 = -0.11785113 Reorder the terms: 1 + x = -0.11785113 Solving 1 + x = -0.11785113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -0.11785113 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.11785113 + -1 x = -0.11785113 + -1 Combine like terms: -0.11785113 + -1 = -1.11785113 x = -1.11785113 Simplifying x = -1.11785113Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.88214887, -1.11785113}
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