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Simplifying x2 + x2 + -20x + 100 = 64 Reorder the terms: 100 + -20x + x2 + x2 = 64 Combine like terms: x2 + x2 = 2x2 100 + -20x + 2x2 = 64 Solving 100 + -20x + 2x2 = 64 Solving for variable 'x'. Reorder the terms: 100 + -64 + -20x + 2x2 = 64 + -64 Combine like terms: 100 + -64 = 36 36 + -20x + 2x2 = 64 + -64 Combine like terms: 64 + -64 = 0 36 + -20x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(18 + -10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + -10x + x2)' equal to zero and attempt to solve: Simplifying 18 + -10x + x2 = 0 Solving 18 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -10x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + -10x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -10x + x2 = 0 + -18 -10x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 -10x + x2 = -18 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -18 + 25 Reorder the terms: 25 + -10x + x2 = -18 + 25 Combine like terms: -18 + 25 = 7 25 + -10x + x2 = 7 Factor a perfect square on the left side: (x + -5)(x + -5) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -5) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -5 = 2.645751311 Simplifying x + -5 = 2.645751311 Reorder the terms: -5 + x = 2.645751311 Solving -5 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.645751311 + 5 x = 2.645751311 + 5 Combine like terms: 2.645751311 + 5 = 7.645751311 x = 7.645751311 Simplifying x = 7.645751311Subproblem 2
x + -5 = -2.645751311 Simplifying x + -5 = -2.645751311 Reorder the terms: -5 + x = -2.645751311 Solving -5 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -2.645751311 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.645751311 + 5 x = -2.645751311 + 5 Combine like terms: -2.645751311 + 5 = 2.354248689 x = 2.354248689 Simplifying x = 2.354248689Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.645751311, 2.354248689}Solution
x = {7.645751311, 2.354248689}
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