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Simplifying 441 = x2 + 20x Reorder the terms: 441 = 20x + x2 Solving 441 = 20x + x2 Solving for variable 'x'. Reorder the terms: 441 + -20x + -1x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 441 + -20x + -1x2 = 0 + x2 + -1x2 441 + -20x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 441 + -20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -441 + 20x + x2 = 0 Move the constant term to the right: Add '441' to each side of the equation. -441 + 20x + 441 + x2 = 0 + 441 Reorder the terms: -441 + 441 + 20x + x2 = 0 + 441 Combine like terms: -441 + 441 = 0 0 + 20x + x2 = 0 + 441 20x + x2 = 0 + 441 Combine like terms: 0 + 441 = 441 20x + x2 = 441 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 441 + 100 Reorder the terms: 100 + 20x + x2 = 441 + 100 Combine like terms: 441 + 100 = 541 100 + 20x + x2 = 541 Factor a perfect square on the left side: (x + 10)(x + 10) = 541 Calculate the square root of the right side: 23.259406699 Break this problem into two subproblems by setting (x + 10) equal to 23.259406699 and -23.259406699.Subproblem 1
x + 10 = 23.259406699 Simplifying x + 10 = 23.259406699 Reorder the terms: 10 + x = 23.259406699 Solving 10 + x = 23.259406699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 23.259406699 + -10 Combine like terms: 10 + -10 = 0 0 + x = 23.259406699 + -10 x = 23.259406699 + -10 Combine like terms: 23.259406699 + -10 = 13.259406699 x = 13.259406699 Simplifying x = 13.259406699Subproblem 2
x + 10 = -23.259406699 Simplifying x + 10 = -23.259406699 Reorder the terms: 10 + x = -23.259406699 Solving 10 + x = -23.259406699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -23.259406699 + -10 Combine like terms: 10 + -10 = 0 0 + x = -23.259406699 + -10 x = -23.259406699 + -10 Combine like terms: -23.259406699 + -10 = -33.259406699 x = -33.259406699 Simplifying x = -33.259406699Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.259406699, -33.259406699}
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