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Simplifying 5.39x2 + -10.27x + 4.22 = 0 Reorder the terms: 4.22 + -10.27x + 5.39x2 = 0 Solving 4.22 + -10.27x + 5.39x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.39 the coefficient of the squared term: Divide each side by '5.39'. 0.7829313544 + -1.905380334x + x2 = 0 Move the constant term to the right: Add '-0.7829313544' to each side of the equation. 0.7829313544 + -1.905380334x + -0.7829313544 + x2 = 0 + -0.7829313544 Reorder the terms: 0.7829313544 + -0.7829313544 + -1.905380334x + x2 = 0 + -0.7829313544 Combine like terms: 0.7829313544 + -0.7829313544 = 0.0000000000 0.0000000000 + -1.905380334x + x2 = 0 + -0.7829313544 -1.905380334x + x2 = 0 + -0.7829313544 Combine like terms: 0 + -0.7829313544 = -0.7829313544 -1.905380334x + x2 = -0.7829313544 The x term is -1.905380334x. Take half its coefficient (-0.952690167). Square it (0.9076185543) and add it to both sides. Add '0.9076185543' to each side of the equation. -1.905380334x + 0.9076185543 + x2 = -0.7829313544 + 0.9076185543 Reorder the terms: 0.9076185543 + -1.905380334x + x2 = -0.7829313544 + 0.9076185543 Combine like terms: -0.7829313544 + 0.9076185543 = 0.1246871999 0.9076185543 + -1.905380334x + x2 = 0.1246871999 Factor a perfect square on the left side: (x + -0.952690167)(x + -0.952690167) = 0.1246871999 Calculate the square root of the right side: 0.353110747 Break this problem into two subproblems by setting (x + -0.952690167) equal to 0.353110747 and -0.353110747.Subproblem 1
x + -0.952690167 = 0.353110747 Simplifying x + -0.952690167 = 0.353110747 Reorder the terms: -0.952690167 + x = 0.353110747 Solving -0.952690167 + x = 0.353110747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.952690167' to each side of the equation. -0.952690167 + 0.952690167 + x = 0.353110747 + 0.952690167 Combine like terms: -0.952690167 + 0.952690167 = 0.000000000 0.000000000 + x = 0.353110747 + 0.952690167 x = 0.353110747 + 0.952690167 Combine like terms: 0.353110747 + 0.952690167 = 1.305800914 x = 1.305800914 Simplifying x = 1.305800914Subproblem 2
x + -0.952690167 = -0.353110747 Simplifying x + -0.952690167 = -0.353110747 Reorder the terms: -0.952690167 + x = -0.353110747 Solving -0.952690167 + x = -0.353110747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.952690167' to each side of the equation. -0.952690167 + 0.952690167 + x = -0.353110747 + 0.952690167 Combine like terms: -0.952690167 + 0.952690167 = 0.000000000 0.000000000 + x = -0.353110747 + 0.952690167 x = -0.353110747 + 0.952690167 Combine like terms: -0.353110747 + 0.952690167 = 0.59957942 x = 0.59957942 Simplifying x = 0.59957942Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.305800914, 0.59957942}
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