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Simplifying 0 = x2 + -42x + 336 Reorder the terms: 0 = 336 + -42x + x2 Solving 0 = 336 + -42x + x2 Solving for variable 'x'. Combine like terms: 0 + -336 = -336 -336 + 42x + -1x2 = 336 + -42x + x2 + -336 + 42x + -1x2 Reorder the terms: -336 + 42x + -1x2 = 336 + -336 + -42x + 42x + x2 + -1x2 Combine like terms: 336 + -336 = 0 -336 + 42x + -1x2 = 0 + -42x + 42x + x2 + -1x2 -336 + 42x + -1x2 = -42x + 42x + x2 + -1x2 Combine like terms: -42x + 42x = 0 -336 + 42x + -1x2 = 0 + x2 + -1x2 -336 + 42x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -336 + 42x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 336 + -42x + x2 = 0 Move the constant term to the right: Add '-336' to each side of the equation. 336 + -42x + -336 + x2 = 0 + -336 Reorder the terms: 336 + -336 + -42x + x2 = 0 + -336 Combine like terms: 336 + -336 = 0 0 + -42x + x2 = 0 + -336 -42x + x2 = 0 + -336 Combine like terms: 0 + -336 = -336 -42x + x2 = -336 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 = -336 + 441 Reorder the terms: 441 + -42x + x2 = -336 + 441 Combine like terms: -336 + 441 = 105 441 + -42x + x2 = 105 Factor a perfect square on the left side: (x + -21)(x + -21) = 105 Calculate the square root of the right side: 10.246950766 Break this problem into two subproblems by setting (x + -21) equal to 10.246950766 and -10.246950766.Subproblem 1
x + -21 = 10.246950766 Simplifying x + -21 = 10.246950766 Reorder the terms: -21 + x = 10.246950766 Solving -21 + x = 10.246950766 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 = 10.246950766 + 21 Combine like terms: -21 + 21 = 0 0 + x = 10.246950766 + 21 x = 10.246950766 + 21 Combine like terms: 10.246950766 + 21 = 31.246950766 x = 31.246950766 Simplifying x = 31.246950766Subproblem 2
x + -21 = -10.246950766 Simplifying x + -21 = -10.246950766 Reorder the terms: -21 + x = -10.246950766 Solving -21 + x = -10.246950766 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 = -10.246950766 + 21 Combine like terms: -21 + 21 = 0 0 + x = -10.246950766 + 21 x = -10.246950766 + 21 Combine like terms: -10.246950766 + 21 = 10.753049234 x = 10.753049234 Simplifying x = 10.753049234Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.246950766, 10.753049234}
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