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Simplifying x2 + -16x + 54 = 0 Reorder the terms: 54 + -16x + x2 = 0 Solving 54 + -16x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-54' to each side of the equation. 54 + -16x + -54 + x2 = 0 + -54 Reorder the terms: 54 + -54 + -16x + x2 = 0 + -54 Combine like terms: 54 + -54 = 0 0 + -16x + x2 = 0 + -54 -16x + x2 = 0 + -54 Combine like terms: 0 + -54 = -54 -16x + x2 = -54 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 = -54 + 64 Reorder the terms: 64 + -16x + x2 = -54 + 64 Combine like terms: -54 + 64 = 10 64 + -16x + x2 = 10 Factor a perfect square on the left side: (x + -8)(x + -8) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -8) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -8 = 3.16227766 Simplifying x + -8 = 3.16227766 Reorder the terms: -8 + x = 3.16227766 Solving -8 + x = 3.16227766 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 = 3.16227766 + 8 Combine like terms: -8 + 8 = 0 0 + x = 3.16227766 + 8 x = 3.16227766 + 8 Combine like terms: 3.16227766 + 8 = 11.16227766 x = 11.16227766 Simplifying x = 11.16227766Subproblem 2
x + -8 = -3.16227766 Simplifying x + -8 = -3.16227766 Reorder the terms: -8 + x = -3.16227766 Solving -8 + x = -3.16227766 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 = -3.16227766 + 8 Combine like terms: -8 + 8 = 0 0 + x = -3.16227766 + 8 x = -3.16227766 + 8 Combine like terms: -3.16227766 + 8 = 4.83772234 x = 4.83772234 Simplifying x = 4.83772234Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.16227766, 4.83772234}
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