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Simplifying 0.04x2 + 5.8x + 4.9 = 0 Reorder the terms: 4.9 + 5.8x + 0.04x2 = 0 Solving 4.9 + 5.8x + 0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.04 the coefficient of the squared term: Divide each side by '0.04'. 122.5 + 145x + x2 = 0 Move the constant term to the right: Add '-122.5' to each side of the equation. 122.5 + 145x + -122.5 + x2 = 0 + -122.5 Reorder the terms: 122.5 + -122.5 + 145x + x2 = 0 + -122.5 Combine like terms: 122.5 + -122.5 = 0.0 0.0 + 145x + x2 = 0 + -122.5 145x + x2 = 0 + -122.5 Combine like terms: 0 + -122.5 = -122.5 145x + x2 = -122.5 The x term is 145x. Take half its coefficient (72.5). Square it (5256.25) and add it to both sides. Add '5256.25' to each side of the equation. 145x + 5256.25 + x2 = -122.5 + 5256.25 Reorder the terms: 5256.25 + 145x + x2 = -122.5 + 5256.25 Combine like terms: -122.5 + 5256.25 = 5133.75 5256.25 + 145x + x2 = 5133.75 Factor a perfect square on the left side: (x + 72.5)(x + 72.5) = 5133.75 Calculate the square root of the right side: 71.650191905 Break this problem into two subproblems by setting (x + 72.5) equal to 71.650191905 and -71.650191905.Subproblem 1
x + 72.5 = 71.650191905 Simplifying x + 72.5 = 71.650191905 Reorder the terms: 72.5 + x = 71.650191905 Solving 72.5 + x = 71.650191905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-72.5' to each side of the equation. 72.5 + -72.5 + x = 71.650191905 + -72.5 Combine like terms: 72.5 + -72.5 = 0.0 0.0 + x = 71.650191905 + -72.5 x = 71.650191905 + -72.5 Combine like terms: 71.650191905 + -72.5 = -0.849808095 x = -0.849808095 Simplifying x = -0.849808095Subproblem 2
x + 72.5 = -71.650191905 Simplifying x + 72.5 = -71.650191905 Reorder the terms: 72.5 + x = -71.650191905 Solving 72.5 + x = -71.650191905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-72.5' to each side of the equation. 72.5 + -72.5 + x = -71.650191905 + -72.5 Combine like terms: 72.5 + -72.5 = 0.0 0.0 + x = -71.650191905 + -72.5 x = -71.650191905 + -72.5 Combine like terms: -71.650191905 + -72.5 = -144.150191905 x = -144.150191905 Simplifying x = -144.150191905Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.849808095, -144.150191905}
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