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Simplifying 0.33x2 + 6x + 10 = 0 Reorder the terms: 10 + 6x + 0.33x2 = 0 Solving 10 + 6x + 0.33x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.33 the coefficient of the squared term: Divide each side by '0.33'. 30.3030303 + 18.18181818x + x2 = 0 Move the constant term to the right: Add '-30.3030303' to each side of the equation. 30.3030303 + 18.18181818x + -30.3030303 + x2 = 0 + -30.3030303 Reorder the terms: 30.3030303 + -30.3030303 + 18.18181818x + x2 = 0 + -30.3030303 Combine like terms: 30.3030303 + -30.3030303 = 0.0000000 0.0000000 + 18.18181818x + x2 = 0 + -30.3030303 18.18181818x + x2 = 0 + -30.3030303 Combine like terms: 0 + -30.3030303 = -30.3030303 18.18181818x + x2 = -30.3030303 The x term is 18.18181818x. Take half its coefficient (9.09090909). Square it (82.64462808) and add it to both sides. Add '82.64462808' to each side of the equation. 18.18181818x + 82.64462808 + x2 = -30.3030303 + 82.64462808 Reorder the terms: 82.64462808 + 18.18181818x + x2 = -30.3030303 + 82.64462808 Combine like terms: -30.3030303 + 82.64462808 = 52.34159778 82.64462808 + 18.18181818x + x2 = 52.34159778 Factor a perfect square on the left side: (x + 9.09090909)(x + 9.09090909) = 52.34159778 Calculate the square root of the right side: 7.234749324 Break this problem into two subproblems by setting (x + 9.09090909) equal to 7.234749324 and -7.234749324.Subproblem 1
x + 9.09090909 = 7.234749324 Simplifying x + 9.09090909 = 7.234749324 Reorder the terms: 9.09090909 + x = 7.234749324 Solving 9.09090909 + x = 7.234749324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.09090909' to each side of the equation. 9.09090909 + -9.09090909 + x = 7.234749324 + -9.09090909 Combine like terms: 9.09090909 + -9.09090909 = 0.00000000 0.00000000 + x = 7.234749324 + -9.09090909 x = 7.234749324 + -9.09090909 Combine like terms: 7.234749324 + -9.09090909 = -1.856159766 x = -1.856159766 Simplifying x = -1.856159766Subproblem 2
x + 9.09090909 = -7.234749324 Simplifying x + 9.09090909 = -7.234749324 Reorder the terms: 9.09090909 + x = -7.234749324 Solving 9.09090909 + x = -7.234749324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.09090909' to each side of the equation. 9.09090909 + -9.09090909 + x = -7.234749324 + -9.09090909 Combine like terms: 9.09090909 + -9.09090909 = 0.00000000 0.00000000 + x = -7.234749324 + -9.09090909 x = -7.234749324 + -9.09090909 Combine like terms: -7.234749324 + -9.09090909 = -16.325658414 x = -16.325658414 Simplifying x = -16.325658414Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.856159766, -16.325658414}
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