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Simplifying x2 + 2x + -37 = 0 Reorder the terms: -37 + 2x + x2 = 0 Solving -37 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + 2x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + 2x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 2x + x2 = 0 + 37 2x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 2x + x2 = 37 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 = 37 + 1 Reorder the terms: 1 + 2x + x2 = 37 + 1 Combine like terms: 37 + 1 = 38 1 + 2x + x2 = 38 Factor a perfect square on the left side: (x + 1)(x + 1) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + 1) equal to 6.164414003 and -6.164414003.Subproblem 1
x + 1 = 6.164414003 Simplifying x + 1 = 6.164414003 Reorder the terms: 1 + x = 6.164414003 Solving 1 + x = 6.164414003 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 = 6.164414003 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.164414003 + -1 x = 6.164414003 + -1 Combine like terms: 6.164414003 + -1 = 5.164414003 x = 5.164414003 Simplifying x = 5.164414003Subproblem 2
x + 1 = -6.164414003 Simplifying x + 1 = -6.164414003 Reorder the terms: 1 + x = -6.164414003 Solving 1 + x = -6.164414003 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 = -6.164414003 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.164414003 + -1 x = -6.164414003 + -1 Combine like terms: -6.164414003 + -1 = -7.164414003 x = -7.164414003 Simplifying x = -7.164414003Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.164414003, -7.164414003}
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