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Simplifying x2 + -42x + 225 = 0 Reorder the terms: 225 + -42x + x2 = 0 Solving 225 + -42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-225' to each side of the equation. 225 + -42x + -225 + x2 = 0 + -225 Reorder the terms: 225 + -225 + -42x + x2 = 0 + -225 Combine like terms: 225 + -225 = 0 0 + -42x + x2 = 0 + -225 -42x + x2 = 0 + -225 Combine like terms: 0 + -225 = -225 -42x + x2 = -225 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 = -225 + 441 Reorder the terms: 441 + -42x + x2 = -225 + 441 Combine like terms: -225 + 441 = 216 441 + -42x + x2 = 216 Factor a perfect square on the left side: (x + -21)(x + -21) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (x + -21) equal to 14.696938457 and -14.696938457.Subproblem 1
x + -21 = 14.696938457 Simplifying x + -21 = 14.696938457 Reorder the terms: -21 + x = 14.696938457 Solving -21 + x = 14.696938457 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 = 14.696938457 + 21 Combine like terms: -21 + 21 = 0 0 + x = 14.696938457 + 21 x = 14.696938457 + 21 Combine like terms: 14.696938457 + 21 = 35.696938457 x = 35.696938457 Simplifying x = 35.696938457Subproblem 2
x + -21 = -14.696938457 Simplifying x + -21 = -14.696938457 Reorder the terms: -21 + x = -14.696938457 Solving -21 + x = -14.696938457 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 = -14.696938457 + 21 Combine like terms: -21 + 21 = 0 0 + x = -14.696938457 + 21 x = -14.696938457 + 21 Combine like terms: -14.696938457 + 21 = 6.303061543 x = 6.303061543 Simplifying x = 6.303061543Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.696938457, 6.303061543}
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