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Simplifying x2 + -42x + 100 = 0 Reorder the terms: 100 + -42x + x2 = 0 Solving 100 + -42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -42x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -42x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -42x + x2 = 0 + -100 -42x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -42x + x2 = -100 The x term is -42x. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42x + 441 + x2 = -100 + 441 Reorder the terms: 441 + -42x + x2 = -100 + 441 Combine like terms: -100 + 441 = 341 441 + -42x + x2 = 341 Factor a perfect square on the left side: (x + -21)(x + -21) = 341 Calculate the square root of the right side: 18.466185313 Break this problem into two subproblems by setting (x + -21) equal to 18.466185313 and -18.466185313.Subproblem 1
x + -21 = 18.466185313 Simplifying x + -21 = 18.466185313 Reorder the terms: -21 + x = 18.466185313 Solving -21 + x = 18.466185313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = 18.466185313 + 21 Combine like terms: -21 + 21 = 0 0 + x = 18.466185313 + 21 x = 18.466185313 + 21 Combine like terms: 18.466185313 + 21 = 39.466185313 x = 39.466185313 Simplifying x = 39.466185313Subproblem 2
x + -21 = -18.466185313 Simplifying x + -21 = -18.466185313 Reorder the terms: -21 + x = -18.466185313 Solving -21 + x = -18.466185313 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + x = -18.466185313 + 21 Combine like terms: -21 + 21 = 0 0 + x = -18.466185313 + 21 x = -18.466185313 + 21 Combine like terms: -18.466185313 + 21 = 2.533814687 x = 2.533814687 Simplifying x = 2.533814687Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.466185313, 2.533814687}
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