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Simplifying 2x2 + 20x + -100 = 49 Reorder the terms: -100 + 20x + 2x2 = 49 Solving -100 + 20x + 2x2 = 49 Solving for variable 'x'. Reorder the terms: -100 + -49 + 20x + 2x2 = 49 + -49 Combine like terms: -100 + -49 = -149 -149 + 20x + 2x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -149 + 20x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -74.5 + 10x + x2 = 0 Move the constant term to the right: Add '74.5' to each side of the equation. -74.5 + 10x + 74.5 + x2 = 0 + 74.5 Reorder the terms: -74.5 + 74.5 + 10x + x2 = 0 + 74.5 Combine like terms: -74.5 + 74.5 = 0.0 0.0 + 10x + x2 = 0 + 74.5 10x + x2 = 0 + 74.5 Combine like terms: 0 + 74.5 = 74.5 10x + x2 = 74.5 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 = 74.5 + 25 Reorder the terms: 25 + 10x + x2 = 74.5 + 25 Combine like terms: 74.5 + 25 = 99.5 25 + 10x + x2 = 99.5 Factor a perfect square on the left side: (x + 5)(x + 5) = 99.5 Calculate the square root of the right side: 9.974968672 Break this problem into two subproblems by setting (x + 5) equal to 9.974968672 and -9.974968672.Subproblem 1
x + 5 = 9.974968672 Simplifying x + 5 = 9.974968672 Reorder the terms: 5 + x = 9.974968672 Solving 5 + x = 9.974968672 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 = 9.974968672 + -5 Combine like terms: 5 + -5 = 0 0 + x = 9.974968672 + -5 x = 9.974968672 + -5 Combine like terms: 9.974968672 + -5 = 4.974968672 x = 4.974968672 Simplifying x = 4.974968672Subproblem 2
x + 5 = -9.974968672 Simplifying x + 5 = -9.974968672 Reorder the terms: 5 + x = -9.974968672 Solving 5 + x = -9.974968672 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 = -9.974968672 + -5 Combine like terms: 5 + -5 = 0 0 + x = -9.974968672 + -5 x = -9.974968672 + -5 Combine like terms: -9.974968672 + -5 = -14.974968672 x = -14.974968672 Simplifying x = -14.974968672Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.974968672, -14.974968672}
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