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Simplifying 176x2 + -3.25x + -5000 = 0 Reorder the terms: -5000 + -3.25x + 176x2 = 0 Solving -5000 + -3.25x + 176x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 176 the coefficient of the squared term: Divide each side by '176'. -28.40909091 + -0.01846590909x + x2 = 0 Move the constant term to the right: Add '28.40909091' to each side of the equation. -28.40909091 + -0.01846590909x + 28.40909091 + x2 = 0 + 28.40909091 Reorder the terms: -28.40909091 + 28.40909091 + -0.01846590909x + x2 = 0 + 28.40909091 Combine like terms: -28.40909091 + 28.40909091 = 0.00000000 0.00000000 + -0.01846590909x + x2 = 0 + 28.40909091 -0.01846590909x + x2 = 0 + 28.40909091 Combine like terms: 0 + 28.40909091 = 28.40909091 -0.01846590909x + x2 = 28.40909091 The x term is -0.01846590909x. Take half its coefficient (-0.009232954545). Square it (0.00008524744963) and add it to both sides. Add '0.00008524744963' to each side of the equation. -0.01846590909x + 0.00008524744963 + x2 = 28.40909091 + 0.00008524744963 Reorder the terms: 0.00008524744963 + -0.01846590909x + x2 = 28.40909091 + 0.00008524744963 Combine like terms: 28.40909091 + 0.00008524744963 = 28.40917615744963 0.00008524744963 + -0.01846590909x + x2 = 28.40917615744963 Factor a perfect square on the left side: (x + -0.009232954545)(x + -0.009232954545) = 28.40917615744963 Calculate the square root of the right side: 5.330025906 Break this problem into two subproblems by setting (x + -0.009232954545) equal to 5.330025906 and -5.330025906.Subproblem 1
x + -0.009232954545 = 5.330025906 Simplifying x + -0.009232954545 = 5.330025906 Reorder the terms: -0.009232954545 + x = 5.330025906 Solving -0.009232954545 + x = 5.330025906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.009232954545' to each side of the equation. -0.009232954545 + 0.009232954545 + x = 5.330025906 + 0.009232954545 Combine like terms: -0.009232954545 + 0.009232954545 = 0.000000000000 0.000000000000 + x = 5.330025906 + 0.009232954545 x = 5.330025906 + 0.009232954545 Combine like terms: 5.330025906 + 0.009232954545 = 5.339258860545 x = 5.339258860545 Simplifying x = 5.339258860545Subproblem 2
x + -0.009232954545 = -5.330025906 Simplifying x + -0.009232954545 = -5.330025906 Reorder the terms: -0.009232954545 + x = -5.330025906 Solving -0.009232954545 + x = -5.330025906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.009232954545' to each side of the equation. -0.009232954545 + 0.009232954545 + x = -5.330025906 + 0.009232954545 Combine like terms: -0.009232954545 + 0.009232954545 = 0.000000000000 0.000000000000 + x = -5.330025906 + 0.009232954545 x = -5.330025906 + 0.009232954545 Combine like terms: -5.330025906 + 0.009232954545 = -5.320792951455 x = -5.320792951455 Simplifying x = -5.320792951455Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.339258860545, -5.320792951455}
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