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Simplifying x2 + 32x + 220 = 3 Reorder the terms: 220 + 32x + x2 = 3 Solving 220 + 32x + x2 = 3 Solving for variable 'x'. Reorder the terms: 220 + -3 + 32x + x2 = 3 + -3 Combine like terms: 220 + -3 = 217 217 + 32x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 217 + 32x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-217' to each side of the equation. 217 + 32x + -217 + x2 = 0 + -217 Reorder the terms: 217 + -217 + 32x + x2 = 0 + -217 Combine like terms: 217 + -217 = 0 0 + 32x + x2 = 0 + -217 32x + x2 = 0 + -217 Combine like terms: 0 + -217 = -217 32x + x2 = -217 The x term is 32x. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32x + 256 + x2 = -217 + 256 Reorder the terms: 256 + 32x + x2 = -217 + 256 Combine like terms: -217 + 256 = 39 256 + 32x + x2 = 39 Factor a perfect square on the left side: (x + 16)(x + 16) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (x + 16) equal to 6.244997998 and -6.244997998.Subproblem 1
x + 16 = 6.244997998 Simplifying x + 16 = 6.244997998 Reorder the terms: 16 + x = 6.244997998 Solving 16 + x = 6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = 6.244997998 + -16 Combine like terms: 16 + -16 = 0 0 + x = 6.244997998 + -16 x = 6.244997998 + -16 Combine like terms: 6.244997998 + -16 = -9.755002002 x = -9.755002002 Simplifying x = -9.755002002Subproblem 2
x + 16 = -6.244997998 Simplifying x + 16 = -6.244997998 Reorder the terms: 16 + x = -6.244997998 Solving 16 + x = -6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + x = -6.244997998 + -16 Combine like terms: 16 + -16 = 0 0 + x = -6.244997998 + -16 x = -6.244997998 + -16 Combine like terms: -6.244997998 + -16 = -22.244997998 x = -22.244997998 Simplifying x = -22.244997998Solution
The solution to the problem is based on the solutions from the subproblems. x = {-9.755002002, -22.244997998}
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