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Simplifying 2x2 + 18x = 100 Reorder the terms: 18x + 2x2 = 100 Solving 18x + 2x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 18x + 2x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 18x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 9x + x2)' equal to zero and attempt to solve: Simplifying -50 + 9x + x2 = 0 Solving -50 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 9x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + 9x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 9x + x2 = 0 + 50 9x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 9x + x2 = 50 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 50 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 50 + 20.25 Combine like terms: 50 + 20.25 = 70.25 20.25 + 9x + x2 = 70.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (x + 4.5) equal to 8.381527307 and -8.381527307.Subproblem 1
x + 4.5 = 8.381527307 Simplifying x + 4.5 = 8.381527307 Reorder the terms: 4.5 + x = 8.381527307 Solving 4.5 + x = 8.381527307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 8.381527307 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 8.381527307 + -4.5 x = 8.381527307 + -4.5 Combine like terms: 8.381527307 + -4.5 = 3.881527307 x = 3.881527307 Simplifying x = 3.881527307Subproblem 2
x + 4.5 = -8.381527307 Simplifying x + 4.5 = -8.381527307 Reorder the terms: 4.5 + x = -8.381527307 Solving 4.5 + x = -8.381527307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -8.381527307 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -8.381527307 + -4.5 x = -8.381527307 + -4.5 Combine like terms: -8.381527307 + -4.5 = -12.881527307 x = -12.881527307 Simplifying x = -12.881527307Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.881527307, -12.881527307}Solution
x = {3.881527307, -12.881527307}
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