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Simplifying 0.5x2 + -4x2 + 5.5x + -1 = 0 Reorder the terms: -1 + 5.5x + 0.5x2 + -4x2 = 0 Combine like terms: 0.5x2 + -4x2 = -3.5x2 -1 + 5.5x + -3.5x2 = 0 Solving -1 + 5.5x + -3.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3.5 the coefficient of the squared term: Divide each side by '-3.5'. 0.2857142857 + -1.571428571x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + -1.571428571x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + -1.571428571x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + -1.571428571x + x2 = 0 + -0.2857142857 -1.571428571x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 -1.571428571x + x2 = -0.2857142857 The x term is -1.571428571x. Take half its coefficient (-0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. -1.571428571x + 0.6173469384 + x2 = -0.2857142857 + 0.6173469384 Reorder the terms: 0.6173469384 + -1.571428571x + x2 = -0.2857142857 + 0.6173469384 Combine like terms: -0.2857142857 + 0.6173469384 = 0.3316326527 0.6173469384 + -1.571428571x + x2 = 0.3316326527 Factor a perfect square on the left side: (x + -0.7857142855)(x + -0.7857142855) = 0.3316326527 Calculate the square root of the right side: 0.575875553 Break this problem into two subproblems by setting (x + -0.7857142855) equal to 0.575875553 and -0.575875553.Subproblem 1
x + -0.7857142855 = 0.575875553 Simplifying x + -0.7857142855 = 0.575875553 Reorder the terms: -0.7857142855 + x = 0.575875553 Solving -0.7857142855 + x = 0.575875553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + x = 0.575875553 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = 0.575875553 + 0.7857142855 x = 0.575875553 + 0.7857142855 Combine like terms: 0.575875553 + 0.7857142855 = 1.3615898385 x = 1.3615898385 Simplifying x = 1.3615898385Subproblem 2
x + -0.7857142855 = -0.575875553 Simplifying x + -0.7857142855 = -0.575875553 Reorder the terms: -0.7857142855 + x = -0.575875553 Solving -0.7857142855 + x = -0.575875553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7857142855' to each side of the equation. -0.7857142855 + 0.7857142855 + x = -0.575875553 + 0.7857142855 Combine like terms: -0.7857142855 + 0.7857142855 = 0.0000000000 0.0000000000 + x = -0.575875553 + 0.7857142855 x = -0.575875553 + 0.7857142855 Combine like terms: -0.575875553 + 0.7857142855 = 0.2098387325 x = 0.2098387325 Simplifying x = 0.2098387325Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3615898385, 0.2098387325}
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