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Simplifying 3(6x + -7) * 15x = 3 Reorder the terms: 3(-7 + 6x) * 15x = 3 Reorder the terms for easier multiplication: 3 * 15x(-7 + 6x) = 3 Multiply 3 * 15 45x(-7 + 6x) = 3 (-7 * 45x + 6x * 45x) = 3 (-315x + 270x2) = 3 Solving -315x + 270x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -315x + 270x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -315x + 270x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-1 + -105x + 90x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-1 + -105x + 90x2)' equal to zero and attempt to solve: Simplifying -1 + -105x + 90x2 = 0 Solving -1 + -105x + 90x2 = 0 Begin completing the square. Divide all terms by 90 the coefficient of the squared term: Divide each side by '90'. -0.01111111111 + -1.166666667x + x2 = 0.0 Move the constant term to the right: Add '0.01111111111' to each side of the equation. -0.01111111111 + -1.166666667x + 0.01111111111 + x2 = 0.0 + 0.01111111111 Reorder the terms: -0.01111111111 + 0.01111111111 + -1.166666667x + x2 = 0.0 + 0.01111111111 Combine like terms: -0.01111111111 + 0.01111111111 = 0.00000000000 0.00000000000 + -1.166666667x + x2 = 0.0 + 0.01111111111 -1.166666667x + x2 = 0.0 + 0.01111111111 Combine like terms: 0.0 + 0.01111111111 = 0.01111111111 -1.166666667x + x2 = 0.01111111111 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 = 0.01111111111 + 0.3402777780 Reorder the terms: 0.3402777780 + -1.166666667x + x2 = 0.01111111111 + 0.3402777780 Combine like terms: 0.01111111111 + 0.3402777780 = 0.35138888911 0.3402777780 + -1.166666667x + x2 = 0.35138888911 Factor a perfect square on the left side: (x + -0.5833333335)(x + -0.5833333335) = 0.35138888911 Calculate the square root of the right side: 0.592780642 Break this problem into two subproblems by setting (x + -0.5833333335) equal to 0.592780642 and -0.592780642.Subproblem 1
x + -0.5833333335 = 0.592780642 Simplifying x + -0.5833333335 = 0.592780642 Reorder the terms: -0.5833333335 + x = 0.592780642 Solving -0.5833333335 + x = 0.592780642 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 = 0.592780642 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = 0.592780642 + 0.5833333335 x = 0.592780642 + 0.5833333335 Combine like terms: 0.592780642 + 0.5833333335 = 1.1761139755 x = 1.1761139755 Simplifying x = 1.1761139755Subproblem 2
x + -0.5833333335 = -0.592780642 Simplifying x + -0.5833333335 = -0.592780642 Reorder the terms: -0.5833333335 + x = -0.592780642 Solving -0.5833333335 + x = -0.592780642 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 = -0.592780642 + 0.5833333335 Combine like terms: -0.5833333335 + 0.5833333335 = 0.0000000000 0.0000000000 + x = -0.592780642 + 0.5833333335 x = -0.592780642 + 0.5833333335 Combine like terms: -0.592780642 + 0.5833333335 = -0.0094473085 x = -0.0094473085 Simplifying x = -0.0094473085Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1761139755, -0.0094473085}Solution
x = {1.1761139755, -0.0094473085}
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