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Simplifying x2 + 14x + 49 = 32 Reorder the terms: 49 + 14x + x2 = 32 Solving 49 + 14x + x2 = 32 Solving for variable 'x'. Reorder the terms: 49 + -32 + 14x + x2 = 32 + -32 Combine like terms: 49 + -32 = 17 17 + 14x + x2 = 32 + -32 Combine like terms: 32 + -32 = 0 17 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + 14x + -17 + x2 = 0 + -17 Reorder the terms: 17 + -17 + 14x + x2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + 14x + x2 = 0 + -17 14x + x2 = 0 + -17 Combine like terms: 0 + -17 = -17 14x + x2 = -17 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -17 + 49 Reorder the terms: 49 + 14x + x2 = -17 + 49 Combine like terms: -17 + 49 = 32 49 + 14x + x2 = 32 Factor a perfect square on the left side: (x + 7)(x + 7) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 7) equal to 5.656854249 and -5.656854249.Subproblem 1
x + 7 = 5.656854249 Simplifying x + 7 = 5.656854249 Reorder the terms: 7 + x = 5.656854249 Solving 7 + x = 5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 5.656854249 + -7 Combine like terms: 7 + -7 = 0 0 + x = 5.656854249 + -7 x = 5.656854249 + -7 Combine like terms: 5.656854249 + -7 = -1.343145751 x = -1.343145751 Simplifying x = -1.343145751Subproblem 2
x + 7 = -5.656854249 Simplifying x + 7 = -5.656854249 Reorder the terms: 7 + x = -5.656854249 Solving 7 + x = -5.656854249 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -5.656854249 + -7 Combine like terms: 7 + -7 = 0 0 + x = -5.656854249 + -7 x = -5.656854249 + -7 Combine like terms: -5.656854249 + -7 = -12.656854249 x = -12.656854249 Simplifying x = -12.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.343145751, -12.656854249}
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