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Simplifying 175 = (2x + 5)(2x + 7) Reorder the terms: 175 = (5 + 2x)(2x + 7) Reorder the terms: 175 = (5 + 2x)(7 + 2x) Multiply (5 + 2x) * (7 + 2x) 175 = (5(7 + 2x) + 2x * (7 + 2x)) 175 = ((7 * 5 + 2x * 5) + 2x * (7 + 2x)) 175 = ((35 + 10x) + 2x * (7 + 2x)) 175 = (35 + 10x + (7 * 2x + 2x * 2x)) 175 = (35 + 10x + (14x + 4x2)) Combine like terms: 10x + 14x = 24x 175 = (35 + 24x + 4x2) Solving 175 = 35 + 24x + 4x2 Solving for variable 'x'. Combine like terms: 175 + -35 = 140 140 + -24x + -4x2 = 35 + 24x + 4x2 + -35 + -24x + -4x2 Reorder the terms: 140 + -24x + -4x2 = 35 + -35 + 24x + -24x + 4x2 + -4x2 Combine like terms: 35 + -35 = 0 140 + -24x + -4x2 = 0 + 24x + -24x + 4x2 + -4x2 140 + -24x + -4x2 = 24x + -24x + 4x2 + -4x2 Combine like terms: 24x + -24x = 0 140 + -24x + -4x2 = 0 + 4x2 + -4x2 140 + -24x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 140 + -24x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(35 + -6x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(35 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 35 + -6x + -1x2 = 0 Solving 35 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -35 + 6x + x2 = 0 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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