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Simplifying 0.014x2 + -1.19x + 23.24 = 0 Reorder the terms: 23.24 + -1.19x + 0.014x2 = 0 Solving 23.24 + -1.19x + 0.014x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.014 the coefficient of the squared term: Divide each side by '0.014'. 1660 + -85x + x2 = 0 Move the constant term to the right: Add '-1660' to each side of the equation. 1660 + -85x + -1660 + x2 = 0 + -1660 Reorder the terms: 1660 + -1660 + -85x + x2 = 0 + -1660 Combine like terms: 1660 + -1660 = 0 0 + -85x + x2 = 0 + -1660 -85x + x2 = 0 + -1660 Combine like terms: 0 + -1660 = -1660 -85x + x2 = -1660 The x term is -85x. Take half its coefficient (-42.5). Square it (1806.25) and add it to both sides. Add '1806.25' to each side of the equation. -85x + 1806.25 + x2 = -1660 + 1806.25 Reorder the terms: 1806.25 + -85x + x2 = -1660 + 1806.25 Combine like terms: -1660 + 1806.25 = 146.25 1806.25 + -85x + x2 = 146.25 Factor a perfect square on the left side: (x + -42.5)(x + -42.5) = 146.25 Calculate the square root of the right side: 12.093386622 Break this problem into two subproblems by setting (x + -42.5) equal to 12.093386622 and -12.093386622.Subproblem 1
x + -42.5 = 12.093386622 Simplifying x + -42.5 = 12.093386622 Reorder the terms: -42.5 + x = 12.093386622 Solving -42.5 + x = 12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.5' to each side of the equation. -42.5 + 42.5 + x = 12.093386622 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + x = 12.093386622 + 42.5 x = 12.093386622 + 42.5 Combine like terms: 12.093386622 + 42.5 = 54.593386622 x = 54.593386622 Simplifying x = 54.593386622Subproblem 2
x + -42.5 = -12.093386622 Simplifying x + -42.5 = -12.093386622 Reorder the terms: -42.5 + x = -12.093386622 Solving -42.5 + x = -12.093386622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '42.5' to each side of the equation. -42.5 + 42.5 + x = -12.093386622 + 42.5 Combine like terms: -42.5 + 42.5 = 0.0 0.0 + x = -12.093386622 + 42.5 x = -12.093386622 + 42.5 Combine like terms: -12.093386622 + 42.5 = 30.406613378 x = 30.406613378 Simplifying x = 30.406613378Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.593386622, 30.406613378}
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