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Simplifying 5x2 + 50x2 + -1x + -10 = 0 Reorder the terms: -10 + -1x + 5x2 + 50x2 = 0 Combine like terms: 5x2 + 50x2 = 55x2 -10 + -1x + 55x2 = 0 Solving -10 + -1x + 55x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 55 the coefficient of the squared term: Divide each side by '55'. -0.1818181818 + -0.01818181818x + x2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + -0.01818181818x + 0.1818181818 + x2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + -0.01818181818x + x2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + -0.01818181818x + x2 = 0 + 0.1818181818 -0.01818181818x + x2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 -0.01818181818x + x2 = 0.1818181818 The x term is -0.01818181818x. Take half its coefficient (-0.00909090909). Square it (0.00008264462808) and add it to both sides. Add '0.00008264462808' to each side of the equation. -0.01818181818x + 0.00008264462808 + x2 = 0.1818181818 + 0.00008264462808 Reorder the terms: 0.00008264462808 + -0.01818181818x + x2 = 0.1818181818 + 0.00008264462808 Combine like terms: 0.1818181818 + 0.00008264462808 = 0.18190082642808 0.00008264462808 + -0.01818181818x + x2 = 0.18190082642808 Factor a perfect square on the left side: (x + -0.00909090909)(x + -0.00909090909) = 0.18190082642808 Calculate the square root of the right side: 0.426498331 Break this problem into two subproblems by setting (x + -0.00909090909) equal to 0.426498331 and -0.426498331.Subproblem 1
x + -0.00909090909 = 0.426498331 Simplifying x + -0.00909090909 = 0.426498331 Reorder the terms: -0.00909090909 + x = 0.426498331 Solving -0.00909090909 + x = 0.426498331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00909090909' to each side of the equation. -0.00909090909 + 0.00909090909 + x = 0.426498331 + 0.00909090909 Combine like terms: -0.00909090909 + 0.00909090909 = 0.00000000000 0.00000000000 + x = 0.426498331 + 0.00909090909 x = 0.426498331 + 0.00909090909 Combine like terms: 0.426498331 + 0.00909090909 = 0.43558924009 x = 0.43558924009 Simplifying x = 0.43558924009Subproblem 2
x + -0.00909090909 = -0.426498331 Simplifying x + -0.00909090909 = -0.426498331 Reorder the terms: -0.00909090909 + x = -0.426498331 Solving -0.00909090909 + x = -0.426498331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00909090909' to each side of the equation. -0.00909090909 + 0.00909090909 + x = -0.426498331 + 0.00909090909 Combine like terms: -0.00909090909 + 0.00909090909 = 0.00000000000 0.00000000000 + x = -0.426498331 + 0.00909090909 x = -0.426498331 + 0.00909090909 Combine like terms: -0.426498331 + 0.00909090909 = -0.41740742191 x = -0.41740742191 Simplifying x = -0.41740742191Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.43558924009, -0.41740742191}
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