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Simplifying x2 + -16x + 64 = 7 Reorder the terms: 64 + -16x + x2 = 7 Solving 64 + -16x + x2 = 7 Solving for variable 'x'. Reorder the terms: 64 + -7 + -16x + x2 = 7 + -7 Combine like terms: 64 + -7 = 57 57 + -16x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 57 + -16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-57' to each side of the equation. 57 + -16x + -57 + x2 = 0 + -57 Reorder the terms: 57 + -57 + -16x + x2 = 0 + -57 Combine like terms: 57 + -57 = 0 0 + -16x + x2 = 0 + -57 -16x + x2 = 0 + -57 Combine like terms: 0 + -57 = -57 -16x + x2 = -57 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 = -57 + 64 Reorder the terms: 64 + -16x + x2 = -57 + 64 Combine like terms: -57 + 64 = 7 64 + -16x + x2 = 7 Factor a perfect square on the left side: (x + -8)(x + -8) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -8) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -8 = 2.645751311 Simplifying x + -8 = 2.645751311 Reorder the terms: -8 + x = 2.645751311 Solving -8 + x = 2.645751311 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 = 2.645751311 + 8 Combine like terms: -8 + 8 = 0 0 + x = 2.645751311 + 8 x = 2.645751311 + 8 Combine like terms: 2.645751311 + 8 = 10.645751311 x = 10.645751311 Simplifying x = 10.645751311Subproblem 2
x + -8 = -2.645751311 Simplifying x + -8 = -2.645751311 Reorder the terms: -8 + x = -2.645751311 Solving -8 + x = -2.645751311 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 = -2.645751311 + 8 Combine like terms: -8 + 8 = 0 0 + x = -2.645751311 + 8 x = -2.645751311 + 8 Combine like terms: -2.645751311 + 8 = 5.354248689 x = 5.354248689 Simplifying x = 5.354248689Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.645751311, 5.354248689}
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