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Simplifying (-5x2 + 2x + -1) + -1(x2 + -5x + -2) = 0 Reorder the terms: (-1 + 2x + -5x2) + -1(x2 + -5x + -2) = 0 Remove parenthesis around (-1 + 2x + -5x2) -1 + 2x + -5x2 + -1(x2 + -5x + -2) = 0 Reorder the terms: -1 + 2x + -5x2 + -1(-2 + -5x + x2) = 0 -1 + 2x + -5x2 + (-2 * -1 + -5x * -1 + x2 * -1) = 0 -1 + 2x + -5x2 + (2 + 5x + -1x2) = 0 Reorder the terms: -1 + 2 + 2x + 5x + -5x2 + -1x2 = 0 Combine like terms: -1 + 2 = 1 1 + 2x + 5x + -5x2 + -1x2 = 0 Combine like terms: 2x + 5x = 7x 1 + 7x + -5x2 + -1x2 = 0 Combine like terms: -5x2 + -1x2 = -6x2 1 + 7x + -6x2 = 0 Solving 1 + 7x + -6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.1666666667 + -1.166666667x + x2 = 0 Move the constant term to the right: Add '0.1666666667' to each side of the equation. -0.1666666667 + -1.166666667x + 0.1666666667 + x2 = 0 + 0.1666666667 Reorder the terms: -0.1666666667 + 0.1666666667 + -1.166666667x + x2 = 0 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + -1.166666667x + x2 = 0 + 0.1666666667 -1.166666667x + x2 = 0 + 0.1666666667 Combine like terms: 0 + 0.1666666667 = 0.1666666667 -1.166666667x + x2 = 0.1666666667 The x term is -1.166666667x. Take half its coefficient (-0.5833333335). Square it (0.3402777780) and add it to both sides. Add '0.3402777780' to each side of the equation. -1.166666667x + 0.3402777780 + x2 = 0.1666666667 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 0.1666666667 + 0.3402777780 Combine like terms: 0.1666666667 + 0.3402777780 = 0.5069444447 0.3402777780 + -1.166666667x + x2 = 0.5069444447 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 0.5069444447 Calculate the square root of the right side: 0.712000312 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 0.712000312 and -0.712000312.Subproblem 1
x + -0.5833333335 = 0.712000312 Simplifying x + -0.5833333335 = 0.712000312 Reorder the terms: -0.5833333335 + x = 0.712000312 Solving -0.5833333335 + x = 0.712000312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = 0.712000312 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 0.712000312 + 0.5833333335 x = 0.712000312 + 0.5833333335 Combine like terms: 0.712000312 + 0.5833333335 = 1.2953336455 x = 1.2953336455 Simplifying x = 1.2953336455Subproblem 2
x + -0.5833333335 = -0.712000312 Simplifying x + -0.5833333335 = -0.712000312 Reorder the terms: -0.5833333335 + x = -0.712000312 Solving -0.5833333335 + x = -0.712000312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5833333335' to each side of the equation. -0.5833333335 + 0.5833333335 + x = -0.712000312 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -0.712000312 + 0.5833333335 x = -0.712000312 + 0.5833333335 Combine like terms: -0.712000312 + 0.5833333335 = -0.1286669785 x = -0.1286669785 Simplifying x = -0.1286669785Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2953336455, -0.1286669785}
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