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Simplifying -0.45x2 + 50x + 19 = 0 Reorder the terms: 19 + 50x + -0.45x2 = 0 Solving 19 + 50x + -0.45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.45 the coefficient of the squared term: Divide each side by '-0.45'. -42.22222222 + -111.1111111x + x2 = 0 Move the constant term to the right: Add '42.22222222' to each side of the equation. -42.22222222 + -111.1111111x + 42.22222222 + x2 = 0 + 42.22222222 Reorder the terms: -42.22222222 + 42.22222222 + -111.1111111x + x2 = 0 + 42.22222222 Combine like terms: -42.22222222 + 42.22222222 = 0.00000000 0.00000000 + -111.1111111x + x2 = 0 + 42.22222222 -111.1111111x + x2 = 0 + 42.22222222 Combine like terms: 0 + 42.22222222 = 42.22222222 -111.1111111x + x2 = 42.22222222 The x term is -111.1111111x. Take half its coefficient (-55.55555555). Square it (3086.419752) and add it to both sides. Add '3086.419752' to each side of the equation. -111.1111111x + 3086.419752 + x2 = 42.22222222 + 3086.419752 Reorder the terms: 3086.419752 + -111.1111111x + x2 = 42.22222222 + 3086.419752 Combine like terms: 42.22222222 + 3086.419752 = 3128.64197422 3086.419752 + -111.1111111x + x2 = 3128.64197422 Factor a perfect square on the left side: (x + -55.55555555)(x + -55.55555555) = 3128.64197422 Calculate the square root of the right side: 55.93426476 Break this problem into two subproblems by setting (x + -55.55555555) equal to 55.93426476 and -55.93426476.Subproblem 1
x + -55.55555555 = 55.93426476 Simplifying x + -55.55555555 = 55.93426476 Reorder the terms: -55.55555555 + x = 55.93426476 Solving -55.55555555 + x = 55.93426476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55.55555555' to each side of the equation. -55.55555555 + 55.55555555 + x = 55.93426476 + 55.55555555 Combine like terms: -55.55555555 + 55.55555555 = 0.00000000 0.00000000 + x = 55.93426476 + 55.55555555 x = 55.93426476 + 55.55555555 Combine like terms: 55.93426476 + 55.55555555 = 111.48982031 x = 111.48982031 Simplifying x = 111.48982031Subproblem 2
x + -55.55555555 = -55.93426476 Simplifying x + -55.55555555 = -55.93426476 Reorder the terms: -55.55555555 + x = -55.93426476 Solving -55.55555555 + x = -55.93426476 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55.55555555' to each side of the equation. -55.55555555 + 55.55555555 + x = -55.93426476 + 55.55555555 Combine like terms: -55.55555555 + 55.55555555 = 0.00000000 0.00000000 + x = -55.93426476 + 55.55555555 x = -55.93426476 + 55.55555555 Combine like terms: -55.93426476 + 55.55555555 = -0.37870921 x = -0.37870921 Simplifying x = -0.37870921Solution
The solution to the problem is based on the solutions from the subproblems. x = {111.48982031, -0.37870921}
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