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Simplifying x(3 + -4x) + -2(x2 + 5x) + 6 = 0 (3 * x + -4x * x) + -2(x2 + 5x) + 6 = 0 (3x + -4x2) + -2(x2 + 5x) + 6 = 0 Reorder the terms: 3x + -4x2 + -2(5x + x2) + 6 = 0 3x + -4x2 + (5x * -2 + x2 * -2) + 6 = 0 3x + -4x2 + (-10x + -2x2) + 6 = 0 Reorder the terms: 6 + 3x + -10x + -4x2 + -2x2 = 0 Combine like terms: 3x + -10x = -7x 6 + -7x + -4x2 + -2x2 = 0 Combine like terms: -4x2 + -2x2 = -6x2 6 + -7x + -6x2 = 0 Solving 6 + -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'. -1 + 1.166666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.166666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.166666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.166666667x + x2 = 0 + 1 1.166666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.166666667x + x2 = 1 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 = 1 + 0.3402777780 Reorder the terms: 0.3402777780 + 1.166666667x + x2 = 1 + 0.3402777780 Combine like terms: 1 + 0.3402777780 = 1.340277778 0.3402777780 + 1.166666667x + x2 = 1.340277778 Factor a perfect square on the left side: (x + 0.5833333335)(x + 0.5833333335) = 1.340277778 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (x + 0.5833333335) equal to 1.157703666 and -1.157703666.Subproblem 1
x + 0.5833333335 = 1.157703666 Simplifying x + 0.5833333335 = 1.157703666 Reorder the terms: 0.5833333335 + x = 1.157703666 Solving 0.5833333335 + x = 1.157703666 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 = 1.157703666 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = 1.157703666 + -0.5833333335 x = 1.157703666 + -0.5833333335 Combine like terms: 1.157703666 + -0.5833333335 = 0.5743703325 x = 0.5743703325 Simplifying x = 0.5743703325Subproblem 2
x + 0.5833333335 = -1.157703666 Simplifying x + 0.5833333335 = -1.157703666 Reorder the terms: 0.5833333335 + x = -1.157703666 Solving 0.5833333335 + x = -1.157703666 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 = -1.157703666 + -0.5833333335 Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000 0.0000000000 + x = -1.157703666 + -0.5833333335 x = -1.157703666 + -0.5833333335 Combine like terms: -1.157703666 + -0.5833333335 = -1.7410369995 x = -1.7410369995 Simplifying x = -1.7410369995Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5743703325, -1.7410369995}
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