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Simplifying (5x + -1)(2x + 3) = 8x Reorder the terms: (-1 + 5x)(2x + 3) = 8x Reorder the terms: (-1 + 5x)(3 + 2x) = 8x Multiply (-1 + 5x) * (3 + 2x) (-1(3 + 2x) + 5x * (3 + 2x)) = 8x ((3 * -1 + 2x * -1) + 5x * (3 + 2x)) = 8x ((-3 + -2x) + 5x * (3 + 2x)) = 8x (-3 + -2x + (3 * 5x + 2x * 5x)) = 8x (-3 + -2x + (15x + 10x2)) = 8x Combine like terms: -2x + 15x = 13x (-3 + 13x + 10x2) = 8x Solving -3 + 13x + 10x2 = 8x Solving for variable 'x'. Reorder the terms: -3 + 13x + -8x + 10x2 = 8x + -8x Combine like terms: 13x + -8x = 5x -3 + 5x + 10x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -3 + 5x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + 0.5x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.5x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.5x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.5x + x2 = 0.0 + 0.3 0.5x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 0.5x + x2 = 0.3 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.3 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.3 + 0.0625 Combine like terms: 0.3 + 0.0625 = 0.3625 0.0625 + 0.5x + x2 = 0.3625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.3625 Calculate the square root of the right side: 0.602079729 Break this problem into two subproblems by setting (x + 0.25) equal to 0.602079729 and -0.602079729.Subproblem 1
x + 0.25 = 0.602079729 Simplifying x + 0.25 = 0.602079729 Reorder the terms: 0.25 + x = 0.602079729 Solving 0.25 + x = 0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.602079729 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.602079729 + -0.25 x = 0.602079729 + -0.25 Combine like terms: 0.602079729 + -0.25 = 0.352079729 x = 0.352079729 Simplifying x = 0.352079729Subproblem 2
x + 0.25 = -0.602079729 Simplifying x + 0.25 = -0.602079729 Reorder the terms: 0.25 + x = -0.602079729 Solving 0.25 + x = -0.602079729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.602079729 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.602079729 + -0.25 x = -0.602079729 + -0.25 Combine like terms: -0.602079729 + -0.25 = -0.852079729 x = -0.852079729 Simplifying x = -0.852079729Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.352079729, -0.852079729}
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