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Simplifying (6x + -5)(x + 1) = 20 Reorder the terms: (-5 + 6x)(x + 1) = 20 Reorder the terms: (-5 + 6x)(1 + x) = 20 Multiply (-5 + 6x) * (1 + x) (-5(1 + x) + 6x * (1 + x)) = 20 ((1 * -5 + x * -5) + 6x * (1 + x)) = 20 ((-5 + -5x) + 6x * (1 + x)) = 20 (-5 + -5x + (1 * 6x + x * 6x)) = 20 (-5 + -5x + (6x + 6x2)) = 20 Combine like terms: -5x + 6x = 1x (-5 + 1x + 6x2) = 20 Solving -5 + 1x + 6x2 = 20 Solving for variable 'x'. Reorder the terms: -5 + -20 + 1x + 6x2 = 20 + -20 Combine like terms: -5 + -20 = -25 -25 + 1x + 6x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -25 + 1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -4.166666667 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '4.166666667' to each side of the equation. -4.166666667 + 0.1666666667x + 4.166666667 + x2 = 0 + 4.166666667 Reorder the terms: -4.166666667 + 4.166666667 + 0.1666666667x + x2 = 0 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + 0.1666666667x + x2 = 0 + 4.166666667 0.1666666667x + x2 = 0 + 4.166666667 Combine like terms: 0 + 4.166666667 = 4.166666667 0.1666666667x + x2 = 4.166666667 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 = 4.166666667 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 4.166666667 + 0.006944444447 Combine like terms: 4.166666667 + 0.006944444447 = 4.173611111447 0.006944444447 + 0.1666666667x + x2 = 4.173611111447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 4.173611111447 Calculate the square root of the right side: 2.042941779 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 2.042941779 and -2.042941779.Subproblem 1
x + 0.08333333335 = 2.042941779 Simplifying x + 0.08333333335 = 2.042941779 Reorder the terms: 0.08333333335 + x = 2.042941779 Solving 0.08333333335 + x = 2.042941779 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 = 2.042941779 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 2.042941779 + -0.08333333335 x = 2.042941779 + -0.08333333335 Combine like terms: 2.042941779 + -0.08333333335 = 1.95960844565 x = 1.95960844565 Simplifying x = 1.95960844565Subproblem 2
x + 0.08333333335 = -2.042941779 Simplifying x + 0.08333333335 = -2.042941779 Reorder the terms: 0.08333333335 + x = -2.042941779 Solving 0.08333333335 + x = -2.042941779 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 = -2.042941779 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -2.042941779 + -0.08333333335 x = -2.042941779 + -0.08333333335 Combine like terms: -2.042941779 + -0.08333333335 = -2.12627511235 x = -2.12627511235 Simplifying x = -2.12627511235Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.95960844565, -2.12627511235}
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