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Simplifying 33x2 + 7x + -8580 = 0 Reorder the terms: -8580 + 7x + 33x2 = 0 Solving -8580 + 7x + 33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 33 the coefficient of the squared term: Divide each side by '33'. -260 + 0.2121212121x + x2 = 0 Move the constant term to the right: Add '260' to each side of the equation. -260 + 0.2121212121x + 260 + x2 = 0 + 260 Reorder the terms: -260 + 260 + 0.2121212121x + x2 = 0 + 260 Combine like terms: -260 + 260 = 0 0 + 0.2121212121x + x2 = 0 + 260 0.2121212121x + x2 = 0 + 260 Combine like terms: 0 + 260 = 260 0.2121212121x + x2 = 260 The x term is 0.2121212121x. Take half its coefficient (0.1060606061). Square it (0.01124885217) and add it to both sides. Add '0.01124885217' to each side of the equation. 0.2121212121x + 0.01124885217 + x2 = 260 + 0.01124885217 Reorder the terms: 0.01124885217 + 0.2121212121x + x2 = 260 + 0.01124885217 Combine like terms: 260 + 0.01124885217 = 260.01124885217 0.01124885217 + 0.2121212121x + x2 = 260.01124885217 Factor a perfect square on the left side: (x + 0.1060606061)(x + 0.1060606061) = 260.01124885217 Calculate the square root of the right side: 16.124864305 Break this problem into two subproblems by setting (x + 0.1060606061) equal to 16.124864305 and -16.124864305.Subproblem 1
x + 0.1060606061 = 16.124864305 Simplifying x + 0.1060606061 = 16.124864305 Reorder the terms: 0.1060606061 + x = 16.124864305 Solving 0.1060606061 + x = 16.124864305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1060606061' to each side of the equation. 0.1060606061 + -0.1060606061 + x = 16.124864305 + -0.1060606061 Combine like terms: 0.1060606061 + -0.1060606061 = 0.0000000000 0.0000000000 + x = 16.124864305 + -0.1060606061 x = 16.124864305 + -0.1060606061 Combine like terms: 16.124864305 + -0.1060606061 = 16.0188036989 x = 16.0188036989 Simplifying x = 16.0188036989Subproblem 2
x + 0.1060606061 = -16.124864305 Simplifying x + 0.1060606061 = -16.124864305 Reorder the terms: 0.1060606061 + x = -16.124864305 Solving 0.1060606061 + x = -16.124864305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1060606061' to each side of the equation. 0.1060606061 + -0.1060606061 + x = -16.124864305 + -0.1060606061 Combine like terms: 0.1060606061 + -0.1060606061 = 0.0000000000 0.0000000000 + x = -16.124864305 + -0.1060606061 x = -16.124864305 + -0.1060606061 Combine like terms: -16.124864305 + -0.1060606061 = -16.2309249111 x = -16.2309249111 Simplifying x = -16.2309249111Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.0188036989, -16.2309249111}
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