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Simplifying 3.184x2 + -26.2528x + 40.96 = 0 Reorder the terms: 40.96 + -26.2528x + 3.184x2 = 0 Solving 40.96 + -26.2528x + 3.184x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.184 the coefficient of the squared term: Divide each side by '3.184'. 12.86432161 + -8.245226131x + x2 = 0 Move the constant term to the right: Add '-12.86432161' to each side of the equation. 12.86432161 + -8.245226131x + -12.86432161 + x2 = 0 + -12.86432161 Reorder the terms: 12.86432161 + -12.86432161 + -8.245226131x + x2 = 0 + -12.86432161 Combine like terms: 12.86432161 + -12.86432161 = 0.00000000 0.00000000 + -8.245226131x + x2 = 0 + -12.86432161 -8.245226131x + x2 = 0 + -12.86432161 Combine like terms: 0 + -12.86432161 = -12.86432161 -8.245226131x + x2 = -12.86432161 The x term is -8.245226131x. Take half its coefficient (-4.122613066). Square it (16.99593849) and add it to both sides. Add '16.99593849' to each side of the equation. -8.245226131x + 16.99593849 + x2 = -12.86432161 + 16.99593849 Reorder the terms: 16.99593849 + -8.245226131x + x2 = -12.86432161 + 16.99593849 Combine like terms: -12.86432161 + 16.99593849 = 4.13161688 16.99593849 + -8.245226131x + x2 = 4.13161688 Factor a perfect square on the left side: (x + -4.122613066)(x + -4.122613066) = 4.13161688 Calculate the square root of the right side: 2.032637912 Break this problem into two subproblems by setting (x + -4.122613066) equal to 2.032637912 and -2.032637912.Subproblem 1
x + -4.122613066 = 2.032637912 Simplifying x + -4.122613066 = 2.032637912 Reorder the terms: -4.122613066 + x = 2.032637912 Solving -4.122613066 + x = 2.032637912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.122613066' to each side of the equation. -4.122613066 + 4.122613066 + x = 2.032637912 + 4.122613066 Combine like terms: -4.122613066 + 4.122613066 = 0.000000000 0.000000000 + x = 2.032637912 + 4.122613066 x = 2.032637912 + 4.122613066 Combine like terms: 2.032637912 + 4.122613066 = 6.155250978 x = 6.155250978 Simplifying x = 6.155250978Subproblem 2
x + -4.122613066 = -2.032637912 Simplifying x + -4.122613066 = -2.032637912 Reorder the terms: -4.122613066 + x = -2.032637912 Solving -4.122613066 + x = -2.032637912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.122613066' to each side of the equation. -4.122613066 + 4.122613066 + x = -2.032637912 + 4.122613066 Combine like terms: -4.122613066 + 4.122613066 = 0.000000000 0.000000000 + x = -2.032637912 + 4.122613066 x = -2.032637912 + 4.122613066 Combine like terms: -2.032637912 + 4.122613066 = 2.089975154 x = 2.089975154 Simplifying x = 2.089975154Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.155250978, 2.089975154}
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