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Simplifying x2 + 14x + 23 = 0 Reorder the terms: 23 + 14x + x2 = 0 Solving 23 + 14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + 14x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + 14x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + 14x + x2 = 0 + -23 14x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 14x + x2 = -23 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 = -23 + 49 Reorder the terms: 49 + 14x + x2 = -23 + 49 Combine like terms: -23 + 49 = 26 49 + 14x + x2 = 26 Factor a perfect square on the left side: (x + 7)(x + 7) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + 7) equal to 5.099019514 and -5.099019514.Subproblem 1
x + 7 = 5.099019514 Simplifying x + 7 = 5.099019514 Reorder the terms: 7 + x = 5.099019514 Solving 7 + x = 5.099019514 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 = 5.099019514 + -7 Combine like terms: 7 + -7 = 0 0 + x = 5.099019514 + -7 x = 5.099019514 + -7 Combine like terms: 5.099019514 + -7 = -1.900980486 x = -1.900980486 Simplifying x = -1.900980486Subproblem 2
x + 7 = -5.099019514 Simplifying x + 7 = -5.099019514 Reorder the terms: 7 + x = -5.099019514 Solving 7 + x = -5.099019514 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 = -5.099019514 + -7 Combine like terms: 7 + -7 = 0 0 + x = -5.099019514 + -7 x = -5.099019514 + -7 Combine like terms: -5.099019514 + -7 = -12.099019514 x = -12.099019514 Simplifying x = -12.099019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.900980486, -12.099019514}
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