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Simplifying 0 = x2 + 36x + -462 Reorder the terms: 0 = -462 + 36x + x2 Solving 0 = -462 + 36x + x2 Solving for variable 'x'. Combine like terms: 0 + 462 = 462 462 + -36x + -1x2 = -462 + 36x + x2 + 462 + -36x + -1x2 Reorder the terms: 462 + -36x + -1x2 = -462 + 462 + 36x + -36x + x2 + -1x2 Combine like terms: -462 + 462 = 0 462 + -36x + -1x2 = 0 + 36x + -36x + x2 + -1x2 462 + -36x + -1x2 = 36x + -36x + x2 + -1x2 Combine like terms: 36x + -36x = 0 462 + -36x + -1x2 = 0 + x2 + -1x2 462 + -36x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 462 + -36x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -462 + 36x + x2 = 0 Move the constant term to the right: Add '462' to each side of the equation. -462 + 36x + 462 + x2 = 0 + 462 Reorder the terms: -462 + 462 + 36x + x2 = 0 + 462 Combine like terms: -462 + 462 = 0 0 + 36x + x2 = 0 + 462 36x + x2 = 0 + 462 Combine like terms: 0 + 462 = 462 36x + x2 = 462 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = 462 + 324 Reorder the terms: 324 + 36x + x2 = 462 + 324 Combine like terms: 462 + 324 = 786 324 + 36x + x2 = 786 Factor a perfect square on the left side: (x + 18)(x + 18) = 786 Calculate the square root of the right side: 28.035691538 Break this problem into two subproblems by setting (x + 18) equal to 28.035691538 and -28.035691538.Subproblem 1
x + 18 = 28.035691538 Simplifying x + 18 = 28.035691538 Reorder the terms: 18 + x = 28.035691538 Solving 18 + x = 28.035691538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 28.035691538 + -18 Combine like terms: 18 + -18 = 0 0 + x = 28.035691538 + -18 x = 28.035691538 + -18 Combine like terms: 28.035691538 + -18 = 10.035691538 x = 10.035691538 Simplifying x = 10.035691538Subproblem 2
x + 18 = -28.035691538 Simplifying x + 18 = -28.035691538 Reorder the terms: 18 + x = -28.035691538 Solving 18 + x = -28.035691538 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -28.035691538 + -18 Combine like terms: 18 + -18 = 0 0 + x = -28.035691538 + -18 x = -28.035691538 + -18 Combine like terms: -28.035691538 + -18 = -46.035691538 x = -46.035691538 Simplifying x = -46.035691538Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.035691538, -46.035691538}
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