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Simplifying (2x + 10)(2x + -3) = 5 Reorder the terms: (10 + 2x)(2x + -3) = 5 Reorder the terms: (10 + 2x)(-3 + 2x) = 5 Multiply (10 + 2x) * (-3 + 2x) (10(-3 + 2x) + 2x * (-3 + 2x)) = 5 ((-3 * 10 + 2x * 10) + 2x * (-3 + 2x)) = 5 ((-30 + 20x) + 2x * (-3 + 2x)) = 5 (-30 + 20x + (-3 * 2x + 2x * 2x)) = 5 (-30 + 20x + (-6x + 4x2)) = 5 Combine like terms: 20x + -6x = 14x (-30 + 14x + 4x2) = 5 Solving -30 + 14x + 4x2 = 5 Solving for variable 'x'. Reorder the terms: -30 + -5 + 14x + 4x2 = 5 + -5 Combine like terms: -30 + -5 = -35 -35 + 14x + 4x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -35 + 14x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.75 + 3.5x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 3.5x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 3.5x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 3.5x + x2 = 0 + 8.75 3.5x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 3.5x + x2 = 8.75 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 8.75 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 8.75 + 3.0625 Combine like terms: 8.75 + 3.0625 = 11.8125 3.0625 + 3.5x + x2 = 11.8125 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 11.8125 Calculate the square root of the right side: 3.436931771 Break this problem into two subproblems by setting (x + 1.75) equal to 3.436931771 and -3.436931771.Subproblem 1
x + 1.75 = 3.436931771 Simplifying x + 1.75 = 3.436931771 Reorder the terms: 1.75 + x = 3.436931771 Solving 1.75 + x = 3.436931771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 3.436931771 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.436931771 + -1.75 x = 3.436931771 + -1.75 Combine like terms: 3.436931771 + -1.75 = 1.686931771 x = 1.686931771 Simplifying x = 1.686931771Subproblem 2
x + 1.75 = -3.436931771 Simplifying x + 1.75 = -3.436931771 Reorder the terms: 1.75 + x = -3.436931771 Solving 1.75 + x = -3.436931771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -3.436931771 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.436931771 + -1.75 x = -3.436931771 + -1.75 Combine like terms: -3.436931771 + -1.75 = -5.186931771 x = -5.186931771 Simplifying x = -5.186931771Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.686931771, -5.186931771}
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