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Simplifying 3594x2 + 5160x + 5846 = 81000 Reorder the terms: 5846 + 5160x + 3594x2 = 81000 Solving 5846 + 5160x + 3594x2 = 81000 Solving for variable 'x'. Reorder the terms: 5846 + -81000 + 5160x + 3594x2 = 81000 + -81000 Combine like terms: 5846 + -81000 = -75154 -75154 + 5160x + 3594x2 = 81000 + -81000 Combine like terms: 81000 + -81000 = 0 -75154 + 5160x + 3594x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-37577 + 2580x + 1797x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-37577 + 2580x + 1797x2)' equal to zero and attempt to solve: Simplifying -37577 + 2580x + 1797x2 = 0 Solving -37577 + 2580x + 1797x2 = 0 Begin completing the square. Divide all terms by 1797 the coefficient of the squared term: Divide each side by '1797'. -20.91096272 + 1.43572621x + x2 = 0 Move the constant term to the right: Add '20.91096272' to each side of the equation. -20.91096272 + 1.43572621x + 20.91096272 + x2 = 0 + 20.91096272 Reorder the terms: -20.91096272 + 20.91096272 + 1.43572621x + x2 = 0 + 20.91096272 Combine like terms: -20.91096272 + 20.91096272 = 0.00000000 0.00000000 + 1.43572621x + x2 = 0 + 20.91096272 1.43572621x + x2 = 0 + 20.91096272 Combine like terms: 0 + 20.91096272 = 20.91096272 1.43572621x + x2 = 20.91096272 The x term is 1.43572621x. Take half its coefficient (0.717863105). Square it (0.5153274375) and add it to both sides. Add '0.5153274375' to each side of the equation. 1.43572621x + 0.5153274375 + x2 = 20.91096272 + 0.5153274375 Reorder the terms: 0.5153274375 + 1.43572621x + x2 = 20.91096272 + 0.5153274375 Combine like terms: 20.91096272 + 0.5153274375 = 21.4262901575 0.5153274375 + 1.43572621x + x2 = 21.4262901575 Factor a perfect square on the left side: (x + 0.717863105)(x + 0.717863105) = 21.4262901575 Calculate the square root of the right side: 4.628854087 Break this problem into two subproblems by setting (x + 0.717863105) equal to 4.628854087 and -4.628854087.Subproblem 1
x + 0.717863105 = 4.628854087 Simplifying x + 0.717863105 = 4.628854087 Reorder the terms: 0.717863105 + x = 4.628854087 Solving 0.717863105 + x = 4.628854087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.717863105' to each side of the equation. 0.717863105 + -0.717863105 + x = 4.628854087 + -0.717863105 Combine like terms: 0.717863105 + -0.717863105 = 0.000000000 0.000000000 + x = 4.628854087 + -0.717863105 x = 4.628854087 + -0.717863105 Combine like terms: 4.628854087 + -0.717863105 = 3.910990982 x = 3.910990982 Simplifying x = 3.910990982Subproblem 2
x + 0.717863105 = -4.628854087 Simplifying x + 0.717863105 = -4.628854087 Reorder the terms: 0.717863105 + x = -4.628854087 Solving 0.717863105 + x = -4.628854087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.717863105' to each side of the equation. 0.717863105 + -0.717863105 + x = -4.628854087 + -0.717863105 Combine like terms: 0.717863105 + -0.717863105 = 0.000000000 0.000000000 + x = -4.628854087 + -0.717863105 x = -4.628854087 + -0.717863105 Combine like terms: -4.628854087 + -0.717863105 = -5.346717192 x = -5.346717192 Simplifying x = -5.346717192Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.910990982, -5.346717192}Solution
x = {3.910990982, -5.346717192}
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