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Simplifying (1.4x2) + -1(5x) + 2.8 = 0 Remove parenthesis around (5x) (1.4x2) + -1 * 5x + 2.8 = 0 Multiply -1 * 5 (1.4x2) + -5x + 2.8 = 0 Reorder the terms: 2.8 + -5x + (1.4x2) = 0 Solving 2.8 + -5x + (1.4x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.4 the coefficient of the squared term: Divide each side by '1.4'. 2 + -3.571428571x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.571428571x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -3.571428571x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.571428571x + x2 = 0 + -2 -3.571428571x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.571428571x + x2 = -2 The x term is -3.571428571x. Take half its coefficient (-1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. -3.571428571x + 3.188775511 + x2 = -2 + 3.188775511 Reorder the terms: 3.188775511 + -3.571428571x + x2 = -2 + 3.188775511 Combine like terms: -2 + 3.188775511 = 1.188775511 3.188775511 + -3.571428571x + x2 = 1.188775511 Factor a perfect square on the left side: ((x) + -1.785714286)((x) + -1.785714286) = 1.188775511 Calculate the square root of the right side: 1.090309823 Break this problem into two subproblems by setting ((x) + -1.785714286) equal to 1.090309823 and -1.090309823.Subproblem 1
(x) + -1.785714286 = 1.090309823 Simplifying (x) + -1.785714286 = 1.090309823 x + -1.785714286 = 1.090309823 Reorder the terms: -1.785714286 + x = 1.090309823 Solving -1.785714286 + x = 1.090309823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = 1.090309823 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = 1.090309823 + 1.785714286 x = 1.090309823 + 1.785714286 Combine like terms: 1.090309823 + 1.785714286 = 2.876024109 x = 2.876024109 Simplifying x = 2.876024109Subproblem 2
(x) + -1.785714286 = -1.090309823 Simplifying (x) + -1.785714286 = -1.090309823 x + -1.785714286 = -1.090309823 Reorder the terms: -1.785714286 + x = -1.090309823 Solving -1.785714286 + x = -1.090309823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.785714286' to each side of the equation. -1.785714286 + 1.785714286 + x = -1.090309823 + 1.785714286 Combine like terms: -1.785714286 + 1.785714286 = 0.000000000 0.000000000 + x = -1.090309823 + 1.785714286 x = -1.090309823 + 1.785714286 Combine like terms: -1.090309823 + 1.785714286 = 0.695404463 x = 0.695404463 Simplifying x = 0.695404463Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.876024109, 0.695404463}
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