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Simplifying (6x + -1)(2x + 5) = (3x + -1)(2 + -6x) Reorder the terms: (-1 + 6x)(2x + 5) = (3x + -1)(2 + -6x) Reorder the terms: (-1 + 6x)(5 + 2x) = (3x + -1)(2 + -6x) Multiply (-1 + 6x) * (5 + 2x) (-1(5 + 2x) + 6x * (5 + 2x)) = (3x + -1)(2 + -6x) ((5 * -1 + 2x * -1) + 6x * (5 + 2x)) = (3x + -1)(2 + -6x) ((-5 + -2x) + 6x * (5 + 2x)) = (3x + -1)(2 + -6x) (-5 + -2x + (5 * 6x + 2x * 6x)) = (3x + -1)(2 + -6x) (-5 + -2x + (30x + 12x2)) = (3x + -1)(2 + -6x) Combine like terms: -2x + 30x = 28x (-5 + 28x + 12x2) = (3x + -1)(2 + -6x) Reorder the terms: -5 + 28x + 12x2 = (-1 + 3x)(2 + -6x) Multiply (-1 + 3x) * (2 + -6x) -5 + 28x + 12x2 = (-1(2 + -6x) + 3x * (2 + -6x)) -5 + 28x + 12x2 = ((2 * -1 + -6x * -1) + 3x * (2 + -6x)) -5 + 28x + 12x2 = ((-2 + 6x) + 3x * (2 + -6x)) -5 + 28x + 12x2 = (-2 + 6x + (2 * 3x + -6x * 3x)) -5 + 28x + 12x2 = (-2 + 6x + (6x + -18x2)) Combine like terms: 6x + 6x = 12x -5 + 28x + 12x2 = (-2 + 12x + -18x2) Solving -5 + 28x + 12x2 = -2 + 12x + -18x2 Solving for variable 'x'. Reorder the terms: -5 + 2 + 28x + -12x + 12x2 + 18x2 = -2 + 12x + -18x2 + 2 + -12x + 18x2 Combine like terms: -5 + 2 = -3 -3 + 28x + -12x + 12x2 + 18x2 = -2 + 12x + -18x2 + 2 + -12x + 18x2 Combine like terms: 28x + -12x = 16x -3 + 16x + 12x2 + 18x2 = -2 + 12x + -18x2 + 2 + -12x + 18x2 Combine like terms: 12x2 + 18x2 = 30x2 -3 + 16x + 30x2 = -2 + 12x + -18x2 + 2 + -12x + 18x2 Reorder the terms: -3 + 16x + 30x2 = -2 + 2 + 12x + -12x + -18x2 + 18x2 Combine like terms: -2 + 2 = 0 -3 + 16x + 30x2 = 0 + 12x + -12x + -18x2 + 18x2 -3 + 16x + 30x2 = 12x + -12x + -18x2 + 18x2 Combine like terms: 12x + -12x = 0 -3 + 16x + 30x2 = 0 + -18x2 + 18x2 -3 + 16x + 30x2 = -18x2 + 18x2 Combine like terms: -18x2 + 18x2 = 0 -3 + 16x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.1 + 0.5333333333x + x2 = 0.0 Move the constant term to the right: Add '0.1' to each side of the equation. -0.1 + 0.5333333333x + 0.1 + x2 = 0.0 + 0.1 Reorder the terms: -0.1 + 0.1 + 0.5333333333x + x2 = 0.0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + 0.5333333333x + x2 = 0.0 + 0.1 0.5333333333x + x2 = 0.0 + 0.1 Combine like terms: 0.0 + 0.1 = 0.1 0.5333333333x + x2 = 0.1 The x term is 0.5333333333x. Take half its coefficient (0.2666666667). Square it (0.07111111113) and add it to both sides. Add '0.07111111113' to each side of the equation. 0.5333333333x + 0.07111111113 + x2 = 0.1 + 0.07111111113 Reorder the terms: 0.07111111113 + 0.5333333333x + x2 = 0.1 + 0.07111111113 Combine like terms: 0.1 + 0.07111111113 = 0.17111111113 0.07111111113 + 0.5333333333x + x2 = 0.17111111113 Factor a perfect square on the left side: (x + 0.2666666667)(x + 0.2666666667) = 0.17111111113 Calculate the square root of the right side: 0.413655788 Break this problem into two subproblems by setting (x + 0.2666666667) equal to 0.413655788 and -0.413655788.Subproblem 1
x + 0.2666666667 = 0.413655788 Simplifying x + 0.2666666667 = 0.413655788 Reorder the terms: 0.2666666667 + x = 0.413655788 Solving 0.2666666667 + x = 0.413655788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2666666667' to each side of the equation. 0.2666666667 + -0.2666666667 + x = 0.413655788 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + x = 0.413655788 + -0.2666666667 x = 0.413655788 + -0.2666666667 Combine like terms: 0.413655788 + -0.2666666667 = 0.1469891213 x = 0.1469891213 Simplifying x = 0.1469891213Subproblem 2
x + 0.2666666667 = -0.413655788 Simplifying x + 0.2666666667 = -0.413655788 Reorder the terms: 0.2666666667 + x = -0.413655788 Solving 0.2666666667 + x = -0.413655788 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2666666667' to each side of the equation. 0.2666666667 + -0.2666666667 + x = -0.413655788 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + x = -0.413655788 + -0.2666666667 x = -0.413655788 + -0.2666666667 Combine like terms: -0.413655788 + -0.2666666667 = -0.6803224547 x = -0.6803224547 Simplifying x = -0.6803224547Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1469891213, -0.6803224547}
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