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Simplifying 434x2 + 43x + 23 = 43 Reorder the terms: 23 + 43x + 434x2 = 43 Solving 23 + 43x + 434x2 = 43 Solving for variable 'x'. Reorder the terms: 23 + -43 + 43x + 434x2 = 43 + -43 Combine like terms: 23 + -43 = -20 -20 + 43x + 434x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -20 + 43x + 434x2 = 0 Begin completing the square. Divide all terms by 434 the coefficient of the squared term: Divide each side by '434'. -0.04608294931 + 0.09907834101x + x2 = 0 Move the constant term to the right: Add '0.04608294931' to each side of the equation. -0.04608294931 + 0.09907834101x + 0.04608294931 + x2 = 0 + 0.04608294931 Reorder the terms: -0.04608294931 + 0.04608294931 + 0.09907834101x + x2 = 0 + 0.04608294931 Combine like terms: -0.04608294931 + 0.04608294931 = 0.00000000000 0.00000000000 + 0.09907834101x + x2 = 0 + 0.04608294931 0.09907834101x + x2 = 0 + 0.04608294931 Combine like terms: 0 + 0.04608294931 = 0.04608294931 0.09907834101x + x2 = 0.04608294931 The x term is 0.09907834101x. Take half its coefficient (0.04953917051). Square it (0.002454129415) and add it to both sides. Add '0.002454129415' to each side of the equation. 0.09907834101x + 0.002454129415 + x2 = 0.04608294931 + 0.002454129415 Reorder the terms: 0.002454129415 + 0.09907834101x + x2 = 0.04608294931 + 0.002454129415 Combine like terms: 0.04608294931 + 0.002454129415 = 0.048537078725 0.002454129415 + 0.09907834101x + x2 = 0.048537078725 Factor a perfect square on the left side: (x + 0.04953917051)(x + 0.04953917051) = 0.048537078725 Calculate the square root of the right side: 0.220311322 Break this problem into two subproblems by setting (x + 0.04953917051) equal to 0.220311322 and -0.220311322.Subproblem 1
x + 0.04953917051 = 0.220311322 Simplifying x + 0.04953917051 = 0.220311322 Reorder the terms: 0.04953917051 + x = 0.220311322 Solving 0.04953917051 + x = 0.220311322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04953917051' to each side of the equation. 0.04953917051 + -0.04953917051 + x = 0.220311322 + -0.04953917051 Combine like terms: 0.04953917051 + -0.04953917051 = 0.00000000000 0.00000000000 + x = 0.220311322 + -0.04953917051 x = 0.220311322 + -0.04953917051 Combine like terms: 0.220311322 + -0.04953917051 = 0.17077215149 x = 0.17077215149 Simplifying x = 0.17077215149Subproblem 2
x + 0.04953917051 = -0.220311322 Simplifying x + 0.04953917051 = -0.220311322 Reorder the terms: 0.04953917051 + x = -0.220311322 Solving 0.04953917051 + x = -0.220311322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04953917051' to each side of the equation. 0.04953917051 + -0.04953917051 + x = -0.220311322 + -0.04953917051 Combine like terms: 0.04953917051 + -0.04953917051 = 0.00000000000 0.00000000000 + x = -0.220311322 + -0.04953917051 x = -0.220311322 + -0.04953917051 Combine like terms: -0.220311322 + -0.04953917051 = -0.26985049251 x = -0.26985049251 Simplifying x = -0.26985049251Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.17077215149, -0.26985049251}
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