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Simplifying x2 + x + -47 = 0 Reorder the terms: -47 + x + x2 = 0 Solving -47 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + x + x2 = 0 + 47 x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 x + x2 = 47 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 47 + 0.25 Reorder the terms: 0.25 + x + x2 = 47 + 0.25 Combine like terms: 47 + 0.25 = 47.25 0.25 + x + x2 = 47.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (x + 0.5) equal to 6.873863542 and -6.873863542.Subproblem 1
x + 0.5 = 6.873863542 Simplifying x + 0.5 = 6.873863542 Reorder the terms: 0.5 + x = 6.873863542 Solving 0.5 + x = 6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.873863542 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.873863542 + -0.5 x = 6.873863542 + -0.5 Combine like terms: 6.873863542 + -0.5 = 6.373863542 x = 6.373863542 Simplifying x = 6.373863542Subproblem 2
x + 0.5 = -6.873863542 Simplifying x + 0.5 = -6.873863542 Reorder the terms: 0.5 + x = -6.873863542 Solving 0.5 + x = -6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.873863542 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.873863542 + -0.5 x = -6.873863542 + -0.5 Combine like terms: -6.873863542 + -0.5 = -7.373863542 x = -7.373863542 Simplifying x = -7.373863542Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.373863542, -7.373863542}
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