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Simplifying 0.0067x2 + 0.15x + -37 = 0 Reorder the terms: -37 + 0.15x + 0.0067x2 = 0 Solving -37 + 0.15x + 0.0067x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0067 the coefficient of the squared term: Divide each side by '0.0067'. -5522.38806 + 22.3880597x + x2 = 0 Move the constant term to the right: Add '5522.38806' to each side of the equation. -5522.38806 + 22.3880597x + 5522.38806 + x2 = 0 + 5522.38806 Reorder the terms: -5522.38806 + 5522.38806 + 22.3880597x + x2 = 0 + 5522.38806 Combine like terms: -5522.38806 + 5522.38806 = 0.00000 0.00000 + 22.3880597x + x2 = 0 + 5522.38806 22.3880597x + x2 = 0 + 5522.38806 Combine like terms: 0 + 5522.38806 = 5522.38806 22.3880597x + x2 = 5522.38806 The x term is 22.3880597x. Take half its coefficient (11.19402985). Square it (125.3063043) and add it to both sides. Add '125.3063043' to each side of the equation. 22.3880597x + 125.3063043 + x2 = 5522.38806 + 125.3063043 Reorder the terms: 125.3063043 + 22.3880597x + x2 = 5522.38806 + 125.3063043 Combine like terms: 5522.38806 + 125.3063043 = 5647.6943643 125.3063043 + 22.3880597x + x2 = 5647.6943643 Factor a perfect square on the left side: (x + 11.19402985)(x + 11.19402985) = 5647.6943643 Calculate the square root of the right side: 75.151143466 Break this problem into two subproblems by setting (x + 11.19402985) equal to 75.151143466 and -75.151143466.Subproblem 1
x + 11.19402985 = 75.151143466 Simplifying x + 11.19402985 = 75.151143466 Reorder the terms: 11.19402985 + x = 75.151143466 Solving 11.19402985 + x = 75.151143466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.19402985' to each side of the equation. 11.19402985 + -11.19402985 + x = 75.151143466 + -11.19402985 Combine like terms: 11.19402985 + -11.19402985 = 0.00000000 0.00000000 + x = 75.151143466 + -11.19402985 x = 75.151143466 + -11.19402985 Combine like terms: 75.151143466 + -11.19402985 = 63.957113616 x = 63.957113616 Simplifying x = 63.957113616Subproblem 2
x + 11.19402985 = -75.151143466 Simplifying x + 11.19402985 = -75.151143466 Reorder the terms: 11.19402985 + x = -75.151143466 Solving 11.19402985 + x = -75.151143466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11.19402985' to each side of the equation. 11.19402985 + -11.19402985 + x = -75.151143466 + -11.19402985 Combine like terms: 11.19402985 + -11.19402985 = 0.00000000 0.00000000 + x = -75.151143466 + -11.19402985 x = -75.151143466 + -11.19402985 Combine like terms: -75.151143466 + -11.19402985 = -86.345173316 x = -86.345173316 Simplifying x = -86.345173316Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.957113616, -86.345173316}
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