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Simplifying (-2 + -3x) + -1[5 + -1(6x2 + 4x + 1)] = 0 Remove parenthesis around (-2 + -3x) -2 + -3x + -1[5 + -1(6x2 + 4x + 1)] = 0 Reorder the terms: -2 + -3x + -1[5 + -1(1 + 4x + 6x2)] = 0 -2 + -3x + -1[5 + (1 * -1 + 4x * -1 + 6x2 * -1)] = 0 -2 + -3x + -1[5 + (-1 + -4x + -6x2)] = 0 Combine like terms: 5 + -1 = 4 -2 + -3x + -1[4 + -4x + -6x2] = 0 -2 + -3x + [4 * -1 + -4x * -1 + -6x2 * -1] = 0 -2 + -3x + [-4 + 4x + 6x2] = 0 Reorder the terms: -2 + -4 + -3x + 4x + 6x2 = 0 Combine like terms: -2 + -4 = -6 -6 + -3x + 4x + 6x2 = 0 Combine like terms: -3x + 4x = 1x -6 + 1x + 6x2 = 0 Solving -6 + 1x + 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'. -1 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.1666666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.1666666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.1666666667x + x2 = 0 + 1 0.1666666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.1666666667x + x2 = 1 The x term is 0.1666666667x. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667x + 0.006944444447 + x2 = 1 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 1 + 0.006944444447 Combine like terms: 1 + 0.006944444447 = 1.006944444447 0.006944444447 + 0.1666666667x + x2 = 1.006944444447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 1.006944444447 Calculate the square root of the right side: 1.003466215 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 1.003466215 and -1.003466215.Subproblem 1
x + 0.08333333335 = 1.003466215 Simplifying x + 0.08333333335 = 1.003466215 Reorder the terms: 0.08333333335 + x = 1.003466215 Solving 0.08333333335 + x = 1.003466215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = 1.003466215 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 1.003466215 + -0.08333333335 x = 1.003466215 + -0.08333333335 Combine like terms: 1.003466215 + -0.08333333335 = 0.92013288165 x = 0.92013288165 Simplifying x = 0.92013288165Subproblem 2
x + 0.08333333335 = -1.003466215 Simplifying x + 0.08333333335 = -1.003466215 Reorder the terms: 0.08333333335 + x = -1.003466215 Solving 0.08333333335 + x = -1.003466215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = -1.003466215 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -1.003466215 + -0.08333333335 x = -1.003466215 + -0.08333333335 Combine like terms: -1.003466215 + -0.08333333335 = -1.08679954835 x = -1.08679954835 Simplifying x = -1.08679954835Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.92013288165, -1.08679954835}
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