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Simplifying x2 + 4x + -37 = 0 Reorder the terms: -37 + 4x + x2 = 0 Solving -37 + 4x + 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 + 4x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + 4x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 4x + x2 = 0 + 37 4x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 4x + x2 = 37 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 37 + 4 Reorder the terms: 4 + 4x + x2 = 37 + 4 Combine like terms: 37 + 4 = 41 4 + 4x + x2 = 41 Factor a perfect square on the left side: (x + 2)(x + 2) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + 2) equal to 6.403124237 and -6.403124237.Subproblem 1
x + 2 = 6.403124237 Simplifying x + 2 = 6.403124237 Reorder the terms: 2 + x = 6.403124237 Solving 2 + x = 6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 6.403124237 + -2 Combine like terms: 2 + -2 = 0 0 + x = 6.403124237 + -2 x = 6.403124237 + -2 Combine like terms: 6.403124237 + -2 = 4.403124237 x = 4.403124237 Simplifying x = 4.403124237Subproblem 2
x + 2 = -6.403124237 Simplifying x + 2 = -6.403124237 Reorder the terms: 2 + x = -6.403124237 Solving 2 + x = -6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -6.403124237 + -2 Combine like terms: 2 + -2 = 0 0 + x = -6.403124237 + -2 x = -6.403124237 + -2 Combine like terms: -6.403124237 + -2 = -8.403124237 x = -8.403124237 Simplifying x = -8.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.403124237, -8.403124237}
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