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Simplifying -4.1x2 + 5x + -0.7 = 0 Reorder the terms: -0.7 + 5x + -4.1x2 = 0 Solving -0.7 + 5x + -4.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.1 the coefficient of the squared term: Divide each side by '-4.1'. 0.1707317073 + -1.219512195x + x2 = 0 Move the constant term to the right: Add '-0.1707317073' to each side of the equation. 0.1707317073 + -1.219512195x + -0.1707317073 + x2 = 0 + -0.1707317073 Reorder the terms: 0.1707317073 + -0.1707317073 + -1.219512195x + x2 = 0 + -0.1707317073 Combine like terms: 0.1707317073 + -0.1707317073 = 0.0000000000 0.0000000000 + -1.219512195x + x2 = 0 + -0.1707317073 -1.219512195x + x2 = 0 + -0.1707317073 Combine like terms: 0 + -0.1707317073 = -0.1707317073 -1.219512195x + x2 = -0.1707317073 The x term is -1.219512195x. Take half its coefficient (-0.6097560975). Square it (0.3718024984) and add it to both sides. Add '0.3718024984' to each side of the equation. -1.219512195x + 0.3718024984 + x2 = -0.1707317073 + 0.3718024984 Reorder the terms: 0.3718024984 + -1.219512195x + x2 = -0.1707317073 + 0.3718024984 Combine like terms: -0.1707317073 + 0.3718024984 = 0.2010707911 0.3718024984 + -1.219512195x + x2 = 0.2010707911 Factor a perfect square on the left side: (x + -0.6097560975)(x + -0.6097560975) = 0.2010707911 Calculate the square root of the right side: 0.448409178 Break this problem into two subproblems by setting (x + -0.6097560975) equal to 0.448409178 and -0.448409178.Subproblem 1
x + -0.6097560975 = 0.448409178 Simplifying x + -0.6097560975 = 0.448409178 Reorder the terms: -0.6097560975 + x = 0.448409178 Solving -0.6097560975 + x = 0.448409178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6097560975' to each side of the equation. -0.6097560975 + 0.6097560975 + x = 0.448409178 + 0.6097560975 Combine like terms: -0.6097560975 + 0.6097560975 = 0.0000000000 0.0000000000 + x = 0.448409178 + 0.6097560975 x = 0.448409178 + 0.6097560975 Combine like terms: 0.448409178 + 0.6097560975 = 1.0581652755 x = 1.0581652755 Simplifying x = 1.0581652755Subproblem 2
x + -0.6097560975 = -0.448409178 Simplifying x + -0.6097560975 = -0.448409178 Reorder the terms: -0.6097560975 + x = -0.448409178 Solving -0.6097560975 + x = -0.448409178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6097560975' to each side of the equation. -0.6097560975 + 0.6097560975 + x = -0.448409178 + 0.6097560975 Combine like terms: -0.6097560975 + 0.6097560975 = 0.0000000000 0.0000000000 + x = -0.448409178 + 0.6097560975 x = -0.448409178 + 0.6097560975 Combine like terms: -0.448409178 + 0.6097560975 = 0.1613469195 x = 0.1613469195 Simplifying x = 0.1613469195Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0581652755, 0.1613469195}
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