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Simplifying x2 + -16x + 23 = 0 Reorder the terms: 23 + -16x + x2 = 0 Solving 23 + -16x + 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 + -16x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + -16x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -16x + x2 = 0 + -23 -16x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 -16x + x2 = -23 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = -23 + 64 Reorder the terms: 64 + -16x + x2 = -23 + 64 Combine like terms: -23 + 64 = 41 64 + -16x + x2 = 41 Factor a perfect square on the left side: (x + -8)(x + -8) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + -8) equal to 6.403124237 and -6.403124237.Subproblem 1
x + -8 = 6.403124237 Simplifying x + -8 = 6.403124237 Reorder the terms: -8 + x = 6.403124237 Solving -8 + x = 6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 6.403124237 + 8 Combine like terms: -8 + 8 = 0 0 + x = 6.403124237 + 8 x = 6.403124237 + 8 Combine like terms: 6.403124237 + 8 = 14.403124237 x = 14.403124237 Simplifying x = 14.403124237Subproblem 2
x + -8 = -6.403124237 Simplifying x + -8 = -6.403124237 Reorder the terms: -8 + x = -6.403124237 Solving -8 + x = -6.403124237 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -6.403124237 + 8 Combine like terms: -8 + 8 = 0 0 + x = -6.403124237 + 8 x = -6.403124237 + 8 Combine like terms: -6.403124237 + 8 = 1.596875763 x = 1.596875763 Simplifying x = 1.596875763Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.403124237, 1.596875763}
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