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Simplifying 305 = (5x + 5)(2x + 5) Reorder the terms: 305 = (5 + 5x)(2x + 5) Reorder the terms: 305 = (5 + 5x)(5 + 2x) Multiply (5 + 5x) * (5 + 2x) 305 = (5(5 + 2x) + 5x * (5 + 2x)) 305 = ((5 * 5 + 2x * 5) + 5x * (5 + 2x)) 305 = ((25 + 10x) + 5x * (5 + 2x)) 305 = (25 + 10x + (5 * 5x + 2x * 5x)) 305 = (25 + 10x + (25x + 10x2)) Combine like terms: 10x + 25x = 35x 305 = (25 + 35x + 10x2) Solving 305 = 25 + 35x + 10x2 Solving for variable 'x'. Combine like terms: 305 + -25 = 280 280 + -35x + -10x2 = 25 + 35x + 10x2 + -25 + -35x + -10x2 Reorder the terms: 280 + -35x + -10x2 = 25 + -25 + 35x + -35x + 10x2 + -10x2 Combine like terms: 25 + -25 = 0 280 + -35x + -10x2 = 0 + 35x + -35x + 10x2 + -10x2 280 + -35x + -10x2 = 35x + -35x + 10x2 + -10x2 Combine like terms: 35x + -35x = 0 280 + -35x + -10x2 = 0 + 10x2 + -10x2 280 + -35x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 280 + -35x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(56 + -7x + -2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(56 + -7x + -2x2)' equal to zero and attempt to solve: Simplifying 56 + -7x + -2x2 = 0 Solving 56 + -7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -28 + 3.5x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 3.5x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 3.5x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 3.5x + x2 = 0 + 28 3.5x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 3.5x + x2 = 28 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 = 28 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 28 + 3.0625 Combine like terms: 28 + 3.0625 = 31.0625 3.0625 + 3.5x + x2 = 31.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 31.0625 Calculate the square root of the right side: 5.573374202 Break this problem into two subproblems by setting (x + 1.75) equal to 5.573374202 and -5.573374202.Subproblem 1
x + 1.75 = 5.573374202 Simplifying x + 1.75 = 5.573374202 Reorder the terms: 1.75 + x = 5.573374202 Solving 1.75 + x = 5.573374202 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 = 5.573374202 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 5.573374202 + -1.75 x = 5.573374202 + -1.75 Combine like terms: 5.573374202 + -1.75 = 3.823374202 x = 3.823374202 Simplifying x = 3.823374202Subproblem 2
x + 1.75 = -5.573374202 Simplifying x + 1.75 = -5.573374202 Reorder the terms: 1.75 + x = -5.573374202 Solving 1.75 + x = -5.573374202 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 = -5.573374202 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -5.573374202 + -1.75 x = -5.573374202 + -1.75 Combine like terms: -5.573374202 + -1.75 = -7.323374202 x = -7.323374202 Simplifying x = -7.323374202Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.823374202, -7.323374202}Solution
x = {3.823374202, -7.323374202}
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