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Simplifying 0.06x2 + 1.83x + 4 = -4 Reorder the terms: 4 + 1.83x + 0.06x2 = -4 Solving 4 + 1.83x + 0.06x2 = -4 Solving for variable 'x'. Reorder the terms: 4 + 4 + 1.83x + 0.06x2 = -4 + 4 Combine like terms: 4 + 4 = 8 8 + 1.83x + 0.06x2 = -4 + 4 Combine like terms: -4 + 4 = 0 8 + 1.83x + 0.06x2 = 0 Begin completing the square. Divide all terms by 0.06 the coefficient of the squared term: Divide each side by '0.06'. 133.3333333 + 30.5x + x2 = 0 Move the constant term to the right: Add '-133.3333333' to each side of the equation. 133.3333333 + 30.5x + -133.3333333 + x2 = 0 + -133.3333333 Reorder the terms: 133.3333333 + -133.3333333 + 30.5x + x2 = 0 + -133.3333333 Combine like terms: 133.3333333 + -133.3333333 = 0.0000000 0.0000000 + 30.5x + x2 = 0 + -133.3333333 30.5x + x2 = 0 + -133.3333333 Combine like terms: 0 + -133.3333333 = -133.3333333 30.5x + x2 = -133.3333333 The x term is 30.5x. Take half its coefficient (15.25). Square it (232.5625) and add it to both sides. Add '232.5625' to each side of the equation. 30.5x + 232.5625 + x2 = -133.3333333 + 232.5625 Reorder the terms: 232.5625 + 30.5x + x2 = -133.3333333 + 232.5625 Combine like terms: -133.3333333 + 232.5625 = 99.2291667 232.5625 + 30.5x + x2 = 99.2291667 Factor a perfect square on the left side: (x + 15.25)(x + 15.25) = 99.2291667 Calculate the square root of the right side: 9.961383774 Break this problem into two subproblems by setting (x + 15.25) equal to 9.961383774 and -9.961383774.Subproblem 1
x + 15.25 = 9.961383774 Simplifying x + 15.25 = 9.961383774 Reorder the terms: 15.25 + x = 9.961383774 Solving 15.25 + x = 9.961383774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.25' to each side of the equation. 15.25 + -15.25 + x = 9.961383774 + -15.25 Combine like terms: 15.25 + -15.25 = 0.00 0.00 + x = 9.961383774 + -15.25 x = 9.961383774 + -15.25 Combine like terms: 9.961383774 + -15.25 = -5.288616226 x = -5.288616226 Simplifying x = -5.288616226Subproblem 2
x + 15.25 = -9.961383774 Simplifying x + 15.25 = -9.961383774 Reorder the terms: 15.25 + x = -9.961383774 Solving 15.25 + x = -9.961383774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.25' to each side of the equation. 15.25 + -15.25 + x = -9.961383774 + -15.25 Combine like terms: 15.25 + -15.25 = 0.00 0.00 + x = -9.961383774 + -15.25 x = -9.961383774 + -15.25 Combine like terms: -9.961383774 + -15.25 = -25.211383774 x = -25.211383774 Simplifying x = -25.211383774Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.288616226, -25.211383774}
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