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Simplifying 2x2 + 20x + -450 = 0 Reorder the terms: -450 + 20x + 2x2 = 0 Solving -450 + 20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-225 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-225 + 10x + x2)' equal to zero and attempt to solve: Simplifying -225 + 10x + x2 = 0 Solving -225 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 10x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 10x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 10x + x2 = 0 + 225 10x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 10x + x2 = 225 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 = 225 + 25 Reorder the terms: 25 + 10x + x2 = 225 + 25 Combine like terms: 225 + 25 = 250 25 + 10x + x2 = 250 Factor a perfect square on the left side: (x + 5)(x + 5) = 250 Calculate the square root of the right side: 15.811388301 Break this problem into two subproblems by setting (x + 5) equal to 15.811388301 and -15.811388301.Subproblem 1
x + 5 = 15.811388301 Simplifying x + 5 = 15.811388301 Reorder the terms: 5 + x = 15.811388301 Solving 5 + x = 15.811388301 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 = 15.811388301 + -5 Combine like terms: 5 + -5 = 0 0 + x = 15.811388301 + -5 x = 15.811388301 + -5 Combine like terms: 15.811388301 + -5 = 10.811388301 x = 10.811388301 Simplifying x = 10.811388301Subproblem 2
x + 5 = -15.811388301 Simplifying x + 5 = -15.811388301 Reorder the terms: 5 + x = -15.811388301 Solving 5 + x = -15.811388301 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 = -15.811388301 + -5 Combine like terms: 5 + -5 = 0 0 + x = -15.811388301 + -5 x = -15.811388301 + -5 Combine like terms: -15.811388301 + -5 = -20.811388301 x = -20.811388301 Simplifying x = -20.811388301Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.811388301, -20.811388301}Solution
x = {10.811388301, -20.811388301}
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