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Simplifying 2x2 + 20x + -100 = 69 Reorder the terms: -100 + 20x + 2x2 = 69 Solving -100 + 20x + 2x2 = 69 Solving for variable 'x'. Reorder the terms: -100 + -69 + 20x + 2x2 = 69 + -69 Combine like terms: -100 + -69 = -169 -169 + 20x + 2x2 = 69 + -69 Combine like terms: 69 + -69 = 0 -169 + 20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -84.5 + 10x + x2 = 0 Move the constant term to the right: Add '84.5' to each side of the equation. -84.5 + 10x + 84.5 + x2 = 0 + 84.5 Reorder the terms: -84.5 + 84.5 + 10x + x2 = 0 + 84.5 Combine like terms: -84.5 + 84.5 = 0.0 0.0 + 10x + x2 = 0 + 84.5 10x + x2 = 0 + 84.5 Combine like terms: 0 + 84.5 = 84.5 10x + x2 = 84.5 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 = 84.5 + 25 Reorder the terms: 25 + 10x + x2 = 84.5 + 25 Combine like terms: 84.5 + 25 = 109.5 25 + 10x + x2 = 109.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 109.5 Calculate the square root of the right side: 10.464224768 Break this problem into two subproblems by setting (x + 5) equal to 10.464224768 and -10.464224768.Subproblem 1
x + 5 = 10.464224768 Simplifying x + 5 = 10.464224768 Reorder the terms: 5 + x = 10.464224768 Solving 5 + x = 10.464224768 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 = 10.464224768 + -5 Combine like terms: 5 + -5 = 0 0 + x = 10.464224768 + -5 x = 10.464224768 + -5 Combine like terms: 10.464224768 + -5 = 5.464224768 x = 5.464224768 Simplifying x = 5.464224768Subproblem 2
x + 5 = -10.464224768 Simplifying x + 5 = -10.464224768 Reorder the terms: 5 + x = -10.464224768 Solving 5 + x = -10.464224768 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 = -10.464224768 + -5 Combine like terms: 5 + -5 = 0 0 + x = -10.464224768 + -5 x = -10.464224768 + -5 Combine like terms: -10.464224768 + -5 = -15.464224768 x = -15.464224768 Simplifying x = -15.464224768Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.464224768, -15.464224768}
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