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Simplifying 45x2 + -28x + -5 = 0 Reorder the terms: -5 + -28x + 45x2 = 0 Solving -5 + -28x + 45x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.1111111111 + -0.6222222222x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -0.6222222222x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -0.6222222222x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -0.6222222222x + x2 = 0 + 0.1111111111 -0.6222222222x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -0.6222222222x + x2 = 0.1111111111 The x term is -0.6222222222x. Take half its coefficient (-0.3111111111). Square it (0.09679012345) and add it to both sides. Add '0.09679012345' to each side of the equation. -0.6222222222x + 0.09679012345 + x2 = 0.1111111111 + 0.09679012345 Reorder the terms: 0.09679012345 + -0.6222222222x + x2 = 0.1111111111 + 0.09679012345 Combine like terms: 0.1111111111 + 0.09679012345 = 0.20790123455 0.09679012345 + -0.6222222222x + x2 = 0.20790123455 Factor a perfect square on the left side: (x + -0.3111111111)(x + -0.3111111111) = 0.20790123455 Calculate the square root of the right side: 0.455961878 Break this problem into two subproblems by setting (x + -0.3111111111) equal to 0.455961878 and -0.455961878.Subproblem 1
x + -0.3111111111 = 0.455961878 Simplifying x + -0.3111111111 = 0.455961878 Reorder the terms: -0.3111111111 + x = 0.455961878 Solving -0.3111111111 + x = 0.455961878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3111111111' to each side of the equation. -0.3111111111 + 0.3111111111 + x = 0.455961878 + 0.3111111111 Combine like terms: -0.3111111111 + 0.3111111111 = 0.0000000000 0.0000000000 + x = 0.455961878 + 0.3111111111 x = 0.455961878 + 0.3111111111 Combine like terms: 0.455961878 + 0.3111111111 = 0.7670729891 x = 0.7670729891 Simplifying x = 0.7670729891Subproblem 2
x + -0.3111111111 = -0.455961878 Simplifying x + -0.3111111111 = -0.455961878 Reorder the terms: -0.3111111111 + x = -0.455961878 Solving -0.3111111111 + x = -0.455961878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3111111111' to each side of the equation. -0.3111111111 + 0.3111111111 + x = -0.455961878 + 0.3111111111 Combine like terms: -0.3111111111 + 0.3111111111 = 0.0000000000 0.0000000000 + x = -0.455961878 + 0.3111111111 x = -0.455961878 + 0.3111111111 Combine like terms: -0.455961878 + 0.3111111111 = -0.1448507669 x = -0.1448507669 Simplifying x = -0.1448507669Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7670729891, -0.1448507669}
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