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Simplifying 3x2 + 72x = 31335 Reorder the terms: 72x + 3x2 = 31335 Solving 72x + 3x2 = 31335 Solving for variable 'x'. Reorder the terms: -31335 + 72x + 3x2 = 31335 + -31335 Combine like terms: 31335 + -31335 = 0 -31335 + 72x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-10445 + 24x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-10445 + 24x + x2)' equal to zero and attempt to solve: Simplifying -10445 + 24x + x2 = 0 Solving -10445 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10445' to each side of the equation. -10445 + 24x + 10445 + x2 = 0 + 10445 Reorder the terms: -10445 + 10445 + 24x + x2 = 0 + 10445 Combine like terms: -10445 + 10445 = 0 0 + 24x + x2 = 0 + 10445 24x + x2 = 0 + 10445 Combine like terms: 0 + 10445 = 10445 24x + x2 = 10445 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 10445 + 144 Reorder the terms: 144 + 24x + x2 = 10445 + 144 Combine like terms: 10445 + 144 = 10589 144 + 24x + x2 = 10589 Factor a perfect square on the left side: (x + 12)(x + 12) = 10589 Calculate the square root of the right side: 102.902866821 Break this problem into two subproblems by setting (x + 12) equal to 102.902866821 and -102.902866821.Subproblem 1
x + 12 = 102.902866821 Simplifying x + 12 = 102.902866821 Reorder the terms: 12 + x = 102.902866821 Solving 12 + x = 102.902866821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 102.902866821 + -12 Combine like terms: 12 + -12 = 0 0 + x = 102.902866821 + -12 x = 102.902866821 + -12 Combine like terms: 102.902866821 + -12 = 90.902866821 x = 90.902866821 Simplifying x = 90.902866821Subproblem 2
x + 12 = -102.902866821 Simplifying x + 12 = -102.902866821 Reorder the terms: 12 + x = -102.902866821 Solving 12 + x = -102.902866821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -102.902866821 + -12 Combine like terms: 12 + -12 = 0 0 + x = -102.902866821 + -12 x = -102.902866821 + -12 Combine like terms: -102.902866821 + -12 = -114.902866821 x = -114.902866821 Simplifying x = -114.902866821Solution
The solution to the problem is based on the solutions from the subproblems. x = {90.902866821, -114.902866821}Solution
x = {90.902866821, -114.902866821}
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