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Simplifying (x + 2)(x)(5) = 140 Reorder the terms: (2 + x)(x)(5) = 140 Reorder the terms for easier multiplication: 5x(2 + x) = 140 (2 * 5x + x * 5x) = 140 (10x + 5x2) = 140 Solving 10x + 5x2 = 140 Solving for variable 'x'. Reorder the terms: -140 + 10x + 5x2 = 140 + -140 Combine like terms: 140 + -140 = 0 -140 + 10x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-28 + 2x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-28 + 2x + x2)' equal to zero and attempt to solve: Simplifying -28 + 2x + x2 = 0 Solving -28 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + 2x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 2x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 2x + x2 = 0 + 28 2x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 2x + x2 = 28 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 28 + 1 Reorder the terms: 1 + 2x + x2 = 28 + 1 Combine like terms: 28 + 1 = 29 1 + 2x + x2 = 29 Factor a perfect square on the left side: (x + 1)(x + 1) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + 1) equal to 5.385164807 and -5.385164807.Subproblem 1
x + 1 = 5.385164807 Simplifying x + 1 = 5.385164807 Reorder the terms: 1 + x = 5.385164807 Solving 1 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 5.385164807 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.385164807 + -1 x = 5.385164807 + -1 Combine like terms: 5.385164807 + -1 = 4.385164807 x = 4.385164807 Simplifying x = 4.385164807Subproblem 2
x + 1 = -5.385164807 Simplifying x + 1 = -5.385164807 Reorder the terms: 1 + x = -5.385164807 Solving 1 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -5.385164807 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.385164807 + -1 x = -5.385164807 + -1 Combine like terms: -5.385164807 + -1 = -6.385164807 x = -6.385164807 Simplifying x = -6.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.385164807, -6.385164807}Solution
x = {4.385164807, -6.385164807}
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