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Simplifying (2x + 7)(2x + 5) = 175 Reorder the terms: (7 + 2x)(2x + 5) = 175 Reorder the terms: (7 + 2x)(5 + 2x) = 175 Multiply (7 + 2x) * (5 + 2x) (7(5 + 2x) + 2x * (5 + 2x)) = 175 ((5 * 7 + 2x * 7) + 2x * (5 + 2x)) = 175 ((35 + 14x) + 2x * (5 + 2x)) = 175 (35 + 14x + (5 * 2x + 2x * 2x)) = 175 (35 + 14x + (10x + 4x2)) = 175 Combine like terms: 14x + 10x = 24x (35 + 24x + 4x2) = 175 Solving 35 + 24x + 4x2 = 175 Solving for variable 'x'. Reorder the terms: 35 + -175 + 24x + 4x2 = 175 + -175 Combine like terms: 35 + -175 = -140 -140 + 24x + 4x2 = 175 + -175 Combine like terms: 175 + -175 = 0 -140 + 24x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-35 + 6x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-35 + 6x + x2)' equal to zero and attempt to solve: Simplifying -35 + 6x + x2 = 0 Solving -35 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 6x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + 6x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 6x + x2 = 0 + 35 6x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 6x + x2 = 35 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 35 + 9 Reorder the terms: 9 + 6x + x2 = 35 + 9 Combine like terms: 35 + 9 = 44 9 + 6x + x2 = 44 Factor a perfect square on the left side: (x + 3)(x + 3) = 44 Calculate the square root of the right side: 6.633249581 Break this problem into two subproblems by setting (x + 3) equal to 6.633249581 and -6.633249581.Subproblem 1
x + 3 = 6.633249581 Simplifying x + 3 = 6.633249581 Reorder the terms: 3 + x = 6.633249581 Solving 3 + x = 6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6.633249581 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6.633249581 + -3 x = 6.633249581 + -3 Combine like terms: 6.633249581 + -3 = 3.633249581 x = 3.633249581 Simplifying x = 3.633249581Subproblem 2
x + 3 = -6.633249581 Simplifying x + 3 = -6.633249581 Reorder the terms: 3 + x = -6.633249581 Solving 3 + x = -6.633249581 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6.633249581 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6.633249581 + -3 x = -6.633249581 + -3 Combine like terms: -6.633249581 + -3 = -9.633249581 x = -9.633249581 Simplifying x = -9.633249581Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.633249581, -9.633249581}Solution
x = {3.633249581, -9.633249581}
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