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Simplifying -1x2 + 42x + -400 = 0 Reorder the terms: -400 + 42x + -1x2 = 0 Solving -400 + 42x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 400 + -42x + x2 = 0 Move the constant term to the right: Add '-400' to each side of the equation. 400 + -42x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + -42x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -42x + x2 = 0 + -400 -42x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 -42x + x2 = -400 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 = -400 + 441 Reorder the terms: 441 + -42x + x2 = -400 + 441 Combine like terms: -400 + 441 = 41 441 + -42x + x2 = 41 Factor a perfect square on the left side: (x + -21)(x + -21) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + -21) equal to 6.403124237 and -6.403124237.Subproblem 1
x + -21 = 6.403124237 Simplifying x + -21 = 6.403124237 Reorder the terms: -21 + x = 6.403124237 Solving -21 + x = 6.403124237 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 = 6.403124237 + 21 Combine like terms: -21 + 21 = 0 0 + x = 6.403124237 + 21 x = 6.403124237 + 21 Combine like terms: 6.403124237 + 21 = 27.403124237 x = 27.403124237 Simplifying x = 27.403124237Subproblem 2
x + -21 = -6.403124237 Simplifying x + -21 = -6.403124237 Reorder the terms: -21 + x = -6.403124237 Solving -21 + x = -6.403124237 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 = -6.403124237 + 21 Combine like terms: -21 + 21 = 0 0 + x = -6.403124237 + 21 x = -6.403124237 + 21 Combine like terms: -6.403124237 + 21 = 14.596875763 x = 14.596875763 Simplifying x = 14.596875763Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.403124237, 14.596875763}
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