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Simplifying x2 + -42x + 63 = 0 Reorder the terms: 63 + -42x + x2 = 0 Solving 63 + -42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + -42x + -63 + x2 = 0 + -63 Reorder the terms: 63 + -63 + -42x + x2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + -42x + x2 = 0 + -63 -42x + x2 = 0 + -63 Combine like terms: 0 + -63 = -63 -42x + x2 = -63 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 = -63 + 441 Reorder the terms: 441 + -42x + x2 = -63 + 441 Combine like terms: -63 + 441 = 378 441 + -42x + x2 = 378 Factor a perfect square on the left side: (x + -21)(x + -21) = 378 Calculate the square root of the right side: 19.442222095 Break this problem into two subproblems by setting (x + -21) equal to 19.442222095 and -19.442222095.Subproblem 1
x + -21 = 19.442222095 Simplifying x + -21 = 19.442222095 Reorder the terms: -21 + x = 19.442222095 Solving -21 + x = 19.442222095 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 = 19.442222095 + 21 Combine like terms: -21 + 21 = 0 0 + x = 19.442222095 + 21 x = 19.442222095 + 21 Combine like terms: 19.442222095 + 21 = 40.442222095 x = 40.442222095 Simplifying x = 40.442222095Subproblem 2
x + -21 = -19.442222095 Simplifying x + -21 = -19.442222095 Reorder the terms: -21 + x = -19.442222095 Solving -21 + x = -19.442222095 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 = -19.442222095 + 21 Combine like terms: -21 + 21 = 0 0 + x = -19.442222095 + 21 x = -19.442222095 + 21 Combine like terms: -19.442222095 + 21 = 1.557777905 x = 1.557777905 Simplifying x = 1.557777905Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.442222095, 1.557777905}
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