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Simplifying 3x2 + -30x = 69 Reorder the terms: -30x + 3x2 = 69 Solving -30x + 3x2 = 69 Solving for variable 'x'. Reorder the terms: -69 + -30x + 3x2 = 69 + -69 Combine like terms: 69 + -69 = 0 -69 + -30x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-23 + -10x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-23 + -10x + x2)' equal to zero and attempt to solve: Simplifying -23 + -10x + x2 = 0 Solving -23 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -10x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -10x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -10x + x2 = 0 + 23 -10x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -10x + x2 = 23 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 = 23 + 25 Reorder the terms: 25 + -10x + x2 = 23 + 25 Combine like terms: 23 + 25 = 48 25 + -10x + x2 = 48 Factor a perfect square on the left side: (x + -5)(x + -5) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + -5) equal to 6.92820323 and -6.92820323.Subproblem 1
x + -5 = 6.92820323 Simplifying x + -5 = 6.92820323 Reorder the terms: -5 + x = 6.92820323 Solving -5 + x = 6.92820323 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 = 6.92820323 + 5 Combine like terms: -5 + 5 = 0 0 + x = 6.92820323 + 5 x = 6.92820323 + 5 Combine like terms: 6.92820323 + 5 = 11.92820323 x = 11.92820323 Simplifying x = 11.92820323Subproblem 2
x + -5 = -6.92820323 Simplifying x + -5 = -6.92820323 Reorder the terms: -5 + x = -6.92820323 Solving -5 + x = -6.92820323 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 = -6.92820323 + 5 Combine like terms: -5 + 5 = 0 0 + x = -6.92820323 + 5 x = -6.92820323 + 5 Combine like terms: -6.92820323 + 5 = -1.92820323 x = -1.92820323 Simplifying x = -1.92820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.92820323, -1.92820323}Solution
x = {11.92820323, -1.92820323}
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