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Simplifying 0.3636x + 3.5454 = -0.03x2 + 3x Reorder the terms: 3.5454 + 0.3636x = -0.03x2 + 3x Reorder the terms: 3.5454 + 0.3636x = 3x + -0.03x2 Solving 3.5454 + 0.3636x = 3x + -0.03x2 Solving for variable 'x'. Combine like terms: 0.3636x + -3x = -2.6364x 3.5454 + -2.6364x + 0.03x2 = 3x + -0.03x2 + -3x + 0.03x2 Reorder the terms: 3.5454 + -2.6364x + 0.03x2 = 3x + -3x + -0.03x2 + 0.03x2 Combine like terms: 3x + -3x = 0 3.5454 + -2.6364x + 0.03x2 = 0 + -0.03x2 + 0.03x2 3.5454 + -2.6364x + 0.03x2 = -0.03x2 + 0.03x2 Combine like terms: -0.03x2 + 0.03x2 = 0.00 3.5454 + -2.6364x + 0.03x2 = 0.00 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. 118.18 + -87.88x + x2 = 0 Move the constant term to the right: Add '-118.18' to each side of the equation. 118.18 + -87.88x + -118.18 + x2 = 0 + -118.18 Reorder the terms: 118.18 + -118.18 + -87.88x + x2 = 0 + -118.18 Combine like terms: 118.18 + -118.18 = 0.00 0.00 + -87.88x + x2 = 0 + -118.18 -87.88x + x2 = 0 + -118.18 Combine like terms: 0 + -118.18 = -118.18 -87.88x + x2 = -118.18 The x term is -87.88x. Take half its coefficient (-43.94). Square it (1930.7236) and add it to both sides. Add '1930.7236' to each side of the equation. -87.88x + 1930.7236 + x2 = -118.18 + 1930.7236 Reorder the terms: 1930.7236 + -87.88x + x2 = -118.18 + 1930.7236 Combine like terms: -118.18 + 1930.7236 = 1812.5436 1930.7236 + -87.88x + x2 = 1812.5436 Factor a perfect square on the left side: (x + -43.94)(x + -43.94) = 1812.5436 Calculate the square root of the right side: 42.573977968 Break this problem into two subproblems by setting (x + -43.94) equal to 42.573977968 and -42.573977968.Subproblem 1
x + -43.94 = 42.573977968 Simplifying x + -43.94 = 42.573977968 Reorder the terms: -43.94 + x = 42.573977968 Solving -43.94 + x = 42.573977968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '43.94' to each side of the equation. -43.94 + 43.94 + x = 42.573977968 + 43.94 Combine like terms: -43.94 + 43.94 = 0.00 0.00 + x = 42.573977968 + 43.94 x = 42.573977968 + 43.94 Combine like terms: 42.573977968 + 43.94 = 86.513977968 x = 86.513977968 Simplifying x = 86.513977968Subproblem 2
x + -43.94 = -42.573977968 Simplifying x + -43.94 = -42.573977968 Reorder the terms: -43.94 + x = -42.573977968 Solving -43.94 + x = -42.573977968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '43.94' to each side of the equation. -43.94 + 43.94 + x = -42.573977968 + 43.94 Combine like terms: -43.94 + 43.94 = 0.00 0.00 + x = -42.573977968 + 43.94 x = -42.573977968 + 43.94 Combine like terms: -42.573977968 + 43.94 = 1.366022032 x = 1.366022032 Simplifying x = 1.366022032Solution
The solution to the problem is based on the solutions from the subproblems. x = {86.513977968, 1.366022032}
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