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Simplifying (4x + 1)(2x + 10) = 20 Reorder the terms: (1 + 4x)(2x + 10) = 20 Reorder the terms: (1 + 4x)(10 + 2x) = 20 Multiply (1 + 4x) * (10 + 2x) (1(10 + 2x) + 4x * (10 + 2x)) = 20 ((10 * 1 + 2x * 1) + 4x * (10 + 2x)) = 20 ((10 + 2x) + 4x * (10 + 2x)) = 20 (10 + 2x + (10 * 4x + 2x * 4x)) = 20 (10 + 2x + (40x + 8x2)) = 20 Combine like terms: 2x + 40x = 42x (10 + 42x + 8x2) = 20 Solving 10 + 42x + 8x2 = 20 Solving for variable 'x'. Reorder the terms: 10 + -20 + 42x + 8x2 = 20 + -20 Combine like terms: 10 + -20 = -10 -10 + 42x + 8x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -10 + 42x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 21x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 21x + 4x2)' equal to zero and attempt to solve: Simplifying -5 + 21x + 4x2 = 0 Solving -5 + 21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 5.25x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 5.25x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 5.25x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 5.25x + x2 = 0 + 1.25 5.25x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 5.25x + x2 = 1.25 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = 1.25 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = 1.25 + 6.890625 Combine like terms: 1.25 + 6.890625 = 8.140625 6.890625 + 5.25x + x2 = 8.140625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 8.140625 Calculate the square root of the right side: 2.853178053 Break this problem into two subproblems by setting (x + 2.625) equal to 2.853178053 and -2.853178053.Subproblem 1
x + 2.625 = 2.853178053 Simplifying x + 2.625 = 2.853178053 Reorder the terms: 2.625 + x = 2.853178053 Solving 2.625 + x = 2.853178053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 2.853178053 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 2.853178053 + -2.625 x = 2.853178053 + -2.625 Combine like terms: 2.853178053 + -2.625 = 0.228178053 x = 0.228178053 Simplifying x = 0.228178053Subproblem 2
x + 2.625 = -2.853178053 Simplifying x + 2.625 = -2.853178053 Reorder the terms: 2.625 + x = -2.853178053 Solving 2.625 + x = -2.853178053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -2.853178053 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -2.853178053 + -2.625 x = -2.853178053 + -2.625 Combine like terms: -2.853178053 + -2.625 = -5.478178053 x = -5.478178053 Simplifying x = -5.478178053Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.228178053, -5.478178053}Solution
x = {0.228178053, -5.478178053}
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