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Simplifying -1.3x2 + 5.1x + -2.2 = 0 Reorder the terms: -2.2 + 5.1x + -1.3x2 = 0 Solving -2.2 + 5.1x + -1.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.3 the coefficient of the squared term: Divide each side by '-1.3'. 1.692307692 + -3.923076923x + x2 = 0 Move the constant term to the right: Add '-1.692307692' to each side of the equation. 1.692307692 + -3.923076923x + -1.692307692 + x2 = 0 + -1.692307692 Reorder the terms: 1.692307692 + -1.692307692 + -3.923076923x + x2 = 0 + -1.692307692 Combine like terms: 1.692307692 + -1.692307692 = 0.000000000 0.000000000 + -3.923076923x + x2 = 0 + -1.692307692 -3.923076923x + x2 = 0 + -1.692307692 Combine like terms: 0 + -1.692307692 = -1.692307692 -3.923076923x + x2 = -1.692307692 The x term is -3.923076923x. Take half its coefficient (-1.961538462). Square it (3.847633138) and add it to both sides. Add '3.847633138' to each side of the equation. -3.923076923x + 3.847633138 + x2 = -1.692307692 + 3.847633138 Reorder the terms: 3.847633138 + -3.923076923x + x2 = -1.692307692 + 3.847633138 Combine like terms: -1.692307692 + 3.847633138 = 2.155325446 3.847633138 + -3.923076923x + x2 = 2.155325446 Factor a perfect square on the left side: (x + -1.961538462)(x + -1.961538462) = 2.155325446 Calculate the square root of the right side: 1.468102669 Break this problem into two subproblems by setting (x + -1.961538462) equal to 1.468102669 and -1.468102669.Subproblem 1
x + -1.961538462 = 1.468102669 Simplifying x + -1.961538462 = 1.468102669 Reorder the terms: -1.961538462 + x = 1.468102669 Solving -1.961538462 + x = 1.468102669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.961538462' to each side of the equation. -1.961538462 + 1.961538462 + x = 1.468102669 + 1.961538462 Combine like terms: -1.961538462 + 1.961538462 = 0.000000000 0.000000000 + x = 1.468102669 + 1.961538462 x = 1.468102669 + 1.961538462 Combine like terms: 1.468102669 + 1.961538462 = 3.429641131 x = 3.429641131 Simplifying x = 3.429641131Subproblem 2
x + -1.961538462 = -1.468102669 Simplifying x + -1.961538462 = -1.468102669 Reorder the terms: -1.961538462 + x = -1.468102669 Solving -1.961538462 + x = -1.468102669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.961538462' to each side of the equation. -1.961538462 + 1.961538462 + x = -1.468102669 + 1.961538462 Combine like terms: -1.961538462 + 1.961538462 = 0.000000000 0.000000000 + x = -1.468102669 + 1.961538462 x = -1.468102669 + 1.961538462 Combine like terms: -1.468102669 + 1.961538462 = 0.493435793 x = 0.493435793 Simplifying x = 0.493435793Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.429641131, 0.493435793}
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