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Simplifying 3.71x2 + -10.45x + 2.71 = 0 Reorder the terms: 2.71 + -10.45x + 3.71x2 = 0 Solving 2.71 + -10.45x + 3.71x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.71 the coefficient of the squared term: Divide each side by '3.71'. 0.730458221 + -2.81671159x + x2 = 0 Move the constant term to the right: Add '-0.730458221' to each side of the equation. 0.730458221 + -2.81671159x + -0.730458221 + x2 = 0 + -0.730458221 Reorder the terms: 0.730458221 + -0.730458221 + -2.81671159x + x2 = 0 + -0.730458221 Combine like terms: 0.730458221 + -0.730458221 = 0.000000000 0.000000000 + -2.81671159x + x2 = 0 + -0.730458221 -2.81671159x + x2 = 0 + -0.730458221 Combine like terms: 0 + -0.730458221 = -0.730458221 -2.81671159x + x2 = -0.730458221 The x term is -2.81671159x. Take half its coefficient (-1.408355795). Square it (1.983466045) and add it to both sides. Add '1.983466045' to each side of the equation. -2.81671159x + 1.983466045 + x2 = -0.730458221 + 1.983466045 Reorder the terms: 1.983466045 + -2.81671159x + x2 = -0.730458221 + 1.983466045 Combine like terms: -0.730458221 + 1.983466045 = 1.253007824 1.983466045 + -2.81671159x + x2 = 1.253007824 Factor a perfect square on the left side: (x + -1.408355795)(x + -1.408355795) = 1.253007824 Calculate the square root of the right side: 1.11937832 Break this problem into two subproblems by setting (x + -1.408355795) equal to 1.11937832 and -1.11937832.Subproblem 1
x + -1.408355795 = 1.11937832 Simplifying x + -1.408355795 = 1.11937832 Reorder the terms: -1.408355795 + x = 1.11937832 Solving -1.408355795 + x = 1.11937832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.408355795' to each side of the equation. -1.408355795 + 1.408355795 + x = 1.11937832 + 1.408355795 Combine like terms: -1.408355795 + 1.408355795 = 0.000000000 0.000000000 + x = 1.11937832 + 1.408355795 x = 1.11937832 + 1.408355795 Combine like terms: 1.11937832 + 1.408355795 = 2.527734115 x = 2.527734115 Simplifying x = 2.527734115Subproblem 2
x + -1.408355795 = -1.11937832 Simplifying x + -1.408355795 = -1.11937832 Reorder the terms: -1.408355795 + x = -1.11937832 Solving -1.408355795 + x = -1.11937832 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.408355795' to each side of the equation. -1.408355795 + 1.408355795 + x = -1.11937832 + 1.408355795 Combine like terms: -1.408355795 + 1.408355795 = 0.000000000 0.000000000 + x = -1.11937832 + 1.408355795 x = -1.11937832 + 1.408355795 Combine like terms: -1.11937832 + 1.408355795 = 0.288977475 x = 0.288977475 Simplifying x = 0.288977475Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.527734115, 0.288977475}
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