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Simplifying -0.0004x2 + 0.148x + -0.191 = 0 Reorder the terms: -0.191 + 0.148x + -0.0004x2 = 0 Solving -0.191 + 0.148x + -0.0004x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0004 the coefficient of the squared term: Divide each side by '-0.0004'. 477.5 + -370x + x2 = 0 Move the constant term to the right: Add '-477.5' to each side of the equation. 477.5 + -370x + -477.5 + x2 = 0 + -477.5 Reorder the terms: 477.5 + -477.5 + -370x + x2 = 0 + -477.5 Combine like terms: 477.5 + -477.5 = 0.0 0.0 + -370x + x2 = 0 + -477.5 -370x + x2 = 0 + -477.5 Combine like terms: 0 + -477.5 = -477.5 -370x + x2 = -477.5 The x term is -370x. Take half its coefficient (-185). Square it (34225) and add it to both sides. Add '34225' to each side of the equation. -370x + 34225 + x2 = -477.5 + 34225 Reorder the terms: 34225 + -370x + x2 = -477.5 + 34225 Combine like terms: -477.5 + 34225 = 33747.5 34225 + -370x + x2 = 33747.5 Factor a perfect square on the left side: (x + -185)(x + -185) = 33747.5 Calculate the square root of the right side: 183.704926445 Break this problem into two subproblems by setting (x + -185) equal to 183.704926445 and -183.704926445.Subproblem 1
x + -185 = 183.704926445 Simplifying x + -185 = 183.704926445 Reorder the terms: -185 + x = 183.704926445 Solving -185 + x = 183.704926445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '185' to each side of the equation. -185 + 185 + x = 183.704926445 + 185 Combine like terms: -185 + 185 = 0 0 + x = 183.704926445 + 185 x = 183.704926445 + 185 Combine like terms: 183.704926445 + 185 = 368.704926445 x = 368.704926445 Simplifying x = 368.704926445Subproblem 2
x + -185 = -183.704926445 Simplifying x + -185 = -183.704926445 Reorder the terms: -185 + x = -183.704926445 Solving -185 + x = -183.704926445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '185' to each side of the equation. -185 + 185 + x = -183.704926445 + 185 Combine like terms: -185 + 185 = 0 0 + x = -183.704926445 + 185 x = -183.704926445 + 185 Combine like terms: -183.704926445 + 185 = 1.295073555 x = 1.295073555 Simplifying x = 1.295073555Solution
The solution to the problem is based on the solutions from the subproblems. x = {368.704926445, 1.295073555}
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