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Simplifying x2 + 46 = -14x Reorder the terms: 46 + x2 = -14x Solving 46 + x2 = -14x Solving for variable 'x'. Reorder the terms: 46 + 14x + x2 = -14x + 14x Combine like terms: -14x + 14x = 0 46 + 14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-46' to each side of the equation. 46 + 14x + -46 + x2 = 0 + -46 Reorder the terms: 46 + -46 + 14x + x2 = 0 + -46 Combine like terms: 46 + -46 = 0 0 + 14x + x2 = 0 + -46 14x + x2 = 0 + -46 Combine like terms: 0 + -46 = -46 14x + x2 = -46 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 = -46 + 49 Reorder the terms: 49 + 14x + x2 = -46 + 49 Combine like terms: -46 + 49 = 3 49 + 14x + x2 = 3 Factor a perfect square on the left side: (x + 7)(x + 7) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 7) equal to 1.732050808 and -1.732050808.Subproblem 1
x + 7 = 1.732050808 Simplifying x + 7 = 1.732050808 Reorder the terms: 7 + x = 1.732050808 Solving 7 + x = 1.732050808 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 = 1.732050808 + -7 Combine like terms: 7 + -7 = 0 0 + x = 1.732050808 + -7 x = 1.732050808 + -7 Combine like terms: 1.732050808 + -7 = -5.267949192 x = -5.267949192 Simplifying x = -5.267949192Subproblem 2
x + 7 = -1.732050808 Simplifying x + 7 = -1.732050808 Reorder the terms: 7 + x = -1.732050808 Solving 7 + x = -1.732050808 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 = -1.732050808 + -7 Combine like terms: 7 + -7 = 0 0 + x = -1.732050808 + -7 x = -1.732050808 + -7 Combine like terms: -1.732050808 + -7 = -8.732050808 x = -8.732050808 Simplifying x = -8.732050808Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.267949192, -8.732050808}
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