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Simplifying 62 = 0.5x2 + 18x Reorder the terms: 62 = 18x + 0.5x2 Solving 62 = 18x + 0.5x2 Solving for variable 'x'. Reorder the terms: 62 + -18x + -0.5x2 = 18x + -18x + 0.5x2 + -0.5x2 Combine like terms: 18x + -18x = 0 62 + -18x + -0.5x2 = 0 + 0.5x2 + -0.5x2 62 + -18x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 62 + -18x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -124 + 36x + x2 = 0 Move the constant term to the right: Add '124' to each side of the equation. -124 + 36x + 124 + x2 = 0 + 124 Reorder the terms: -124 + 124 + 36x + x2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + 36x + x2 = 0 + 124 36x + x2 = 0 + 124 Combine like terms: 0 + 124 = 124 36x + x2 = 124 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 = 124 + 324 Reorder the terms: 324 + 36x + x2 = 124 + 324 Combine like terms: 124 + 324 = 448 324 + 36x + x2 = 448 Factor a perfect square on the left side: (x + 18)(x + 18) = 448 Calculate the square root of the right side: 21.166010489 Break this problem into two subproblems by setting (x + 18) equal to 21.166010489 and -21.166010489.Subproblem 1
x + 18 = 21.166010489 Simplifying x + 18 = 21.166010489 Reorder the terms: 18 + x = 21.166010489 Solving 18 + x = 21.166010489 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 = 21.166010489 + -18 Combine like terms: 18 + -18 = 0 0 + x = 21.166010489 + -18 x = 21.166010489 + -18 Combine like terms: 21.166010489 + -18 = 3.166010489 x = 3.166010489 Simplifying x = 3.166010489Subproblem 2
x + 18 = -21.166010489 Simplifying x + 18 = -21.166010489 Reorder the terms: 18 + x = -21.166010489 Solving 18 + x = -21.166010489 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 = -21.166010489 + -18 Combine like terms: 18 + -18 = 0 0 + x = -21.166010489 + -18 x = -21.166010489 + -18 Combine like terms: -21.166010489 + -18 = -39.166010489 x = -39.166010489 Simplifying x = -39.166010489Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.166010489, -39.166010489}
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