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Simplifying 2X2 + 20X + -3 = 0 Reorder the terms: -3 + 20X + 2X2 = 0 Solving -3 + 20X + 2X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + 10X + X2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 10X + 1.5 + X2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 10X + X2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 10X + X2 = 0 + 1.5 10X + X2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 10X + X2 = 1.5 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 = 1.5 + 25 Reorder the terms: 25 + 10X + X2 = 1.5 + 25 Combine like terms: 1.5 + 25 = 26.5 25 + 10X + X2 = 26.5 Factor a perfect square on the left side: (X + 5)(X + 5) = 26.5 Calculate the square root of the right side: 5.14781507 Break this problem into two subproblems by setting (X + 5) equal to 5.14781507 and -5.14781507.Subproblem 1
X + 5 = 5.14781507 Simplifying X + 5 = 5.14781507 Reorder the terms: 5 + X = 5.14781507 Solving 5 + X = 5.14781507 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 = 5.14781507 + -5 Combine like terms: 5 + -5 = 0 0 + X = 5.14781507 + -5 X = 5.14781507 + -5 Combine like terms: 5.14781507 + -5 = 0.14781507 X = 0.14781507 Simplifying X = 0.14781507Subproblem 2
X + 5 = -5.14781507 Simplifying X + 5 = -5.14781507 Reorder the terms: 5 + X = -5.14781507 Solving 5 + X = -5.14781507 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 = -5.14781507 + -5 Combine like terms: 5 + -5 = 0 0 + X = -5.14781507 + -5 X = -5.14781507 + -5 Combine like terms: -5.14781507 + -5 = -10.14781507 X = -10.14781507 Simplifying X = -10.14781507Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.14781507, -10.14781507}
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