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Simplifying 2x2 + 20x + -190 = 0 Reorder the terms: -190 + 20x + 2x2 = 0 Solving -190 + 20x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-95 + 10x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-95 + 10x + x2)' equal to zero and attempt to solve: Simplifying -95 + 10x + x2 = 0 Solving -95 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '95' to each side of the equation. -95 + 10x + 95 + x2 = 0 + 95 Reorder the terms: -95 + 95 + 10x + x2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + 10x + x2 = 0 + 95 10x + x2 = 0 + 95 Combine like terms: 0 + 95 = 95 10x + x2 = 95 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 = 95 + 25 Reorder the terms: 25 + 10x + x2 = 95 + 25 Combine like terms: 95 + 25 = 120 25 + 10x + x2 = 120 Factor a perfect square on the left side: (x + 5)(x + 5) = 120 Calculate the square root of the right side: 10.95445115 Break this problem into two subproblems by setting (x + 5) equal to 10.95445115 and -10.95445115.Subproblem 1
x + 5 = 10.95445115 Simplifying x + 5 = 10.95445115 Reorder the terms: 5 + x = 10.95445115 Solving 5 + x = 10.95445115 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 = 10.95445115 + -5 Combine like terms: 5 + -5 = 0 0 + x = 10.95445115 + -5 x = 10.95445115 + -5 Combine like terms: 10.95445115 + -5 = 5.95445115 x = 5.95445115 Simplifying x = 5.95445115Subproblem 2
x + 5 = -10.95445115 Simplifying x + 5 = -10.95445115 Reorder the terms: 5 + x = -10.95445115 Solving 5 + x = -10.95445115 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 = -10.95445115 + -5 Combine like terms: 5 + -5 = 0 0 + x = -10.95445115 + -5 x = -10.95445115 + -5 Combine like terms: -10.95445115 + -5 = -15.95445115 x = -15.95445115 Simplifying x = -15.95445115Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.95445115, -15.95445115}Solution
x = {5.95445115, -15.95445115}
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