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Simplifying 0.1x2 + 54x = 1000 Reorder the terms: 54x + 0.1x2 = 1000 Solving 54x + 0.1x2 = 1000 Solving for variable 'x'. Reorder the terms: -1000 + 54x + 0.1x2 = 1000 + -1000 Combine like terms: 1000 + -1000 = 0 -1000 + 54x + 0.1x2 = 0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. -10000 + 540x + x2 = 0 Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 540x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 540x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 540x + x2 = 0 + 10000 540x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 540x + x2 = 10000 The x term is 540x. Take half its coefficient (270). Square it (72900) and add it to both sides. Add '72900' to each side of the equation. 540x + 72900 + x2 = 10000 + 72900 Reorder the terms: 72900 + 540x + x2 = 10000 + 72900 Combine like terms: 10000 + 72900 = 82900 72900 + 540x + x2 = 82900 Factor a perfect square on the left side: (x + 270)(x + 270) = 82900 Calculate the square root of the right side: 287.923600978 Break this problem into two subproblems by setting (x + 270) equal to 287.923600978 and -287.923600978.Subproblem 1
x + 270 = 287.923600978 Simplifying x + 270 = 287.923600978 Reorder the terms: 270 + x = 287.923600978 Solving 270 + x = 287.923600978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-270' to each side of the equation. 270 + -270 + x = 287.923600978 + -270 Combine like terms: 270 + -270 = 0 0 + x = 287.923600978 + -270 x = 287.923600978 + -270 Combine like terms: 287.923600978 + -270 = 17.923600978 x = 17.923600978 Simplifying x = 17.923600978Subproblem 2
x + 270 = -287.923600978 Simplifying x + 270 = -287.923600978 Reorder the terms: 270 + x = -287.923600978 Solving 270 + x = -287.923600978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-270' to each side of the equation. 270 + -270 + x = -287.923600978 + -270 Combine like terms: 270 + -270 = 0 0 + x = -287.923600978 + -270 x = -287.923600978 + -270 Combine like terms: -287.923600978 + -270 = -557.923600978 x = -557.923600978 Simplifying x = -557.923600978Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.923600978, -557.923600978}
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