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Simplifying 30(x + -10) * x = 120 Reorder the terms: 30(-10 + x) * x = 120 Reorder the terms for easier multiplication: 30x(-10 + x) = 120 (-10 * 30x + x * 30x) = 120 (-300x + 30x2) = 120 Solving -300x + 30x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + -300x + 30x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + -300x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '30'. 30(-4 + -10x + x2) = 0 Ignore the factor 30.Subproblem 1
Set the factor '(-4 + -10x + x2)' equal to zero and attempt to solve: Simplifying -4 + -10x + x2 = 0 Solving -4 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -10x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -10x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -10x + x2 = 0 + 4 -10x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -10x + x2 = 4 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 4 + 25 Reorder the terms: 25 + -10x + x2 = 4 + 25 Combine like terms: 4 + 25 = 29 25 + -10x + x2 = 29 Factor a perfect square on the left side: (x + -5)(x + -5) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (x + -5) equal to 5.385164807 and -5.385164807.Subproblem 1
x + -5 = 5.385164807 Simplifying x + -5 = 5.385164807 Reorder the terms: -5 + x = 5.385164807 Solving -5 + x = 5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.385164807 + 5 x = 5.385164807 + 5 Combine like terms: 5.385164807 + 5 = 10.385164807 x = 10.385164807 Simplifying x = 10.385164807Subproblem 2
x + -5 = -5.385164807 Simplifying x + -5 = -5.385164807 Reorder the terms: -5 + x = -5.385164807 Solving -5 + x = -5.385164807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.385164807 + 5 x = -5.385164807 + 5 Combine like terms: -5.385164807 + 5 = -0.385164807 x = -0.385164807 Simplifying x = -0.385164807Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.385164807, -0.385164807}Solution
x = {10.385164807, -0.385164807}
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