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Simplifying (2x2 + -5x + 17) + (8x2 + 9x + -72) = 0 Reorder the terms: (17 + -5x + 2x2) + (8x2 + 9x + -72) = 0 Remove parenthesis around (17 + -5x + 2x2) 17 + -5x + 2x2 + (8x2 + 9x + -72) = 0 Reorder the terms: 17 + -5x + 2x2 + (-72 + 9x + 8x2) = 0 Remove parenthesis around (-72 + 9x + 8x2) 17 + -5x + 2x2 + -72 + 9x + 8x2 = 0 Reorder the terms: 17 + -72 + -5x + 9x + 2x2 + 8x2 = 0 Combine like terms: 17 + -72 = -55 -55 + -5x + 9x + 2x2 + 8x2 = 0 Combine like terms: -5x + 9x = 4x -55 + 4x + 2x2 + 8x2 = 0 Combine like terms: 2x2 + 8x2 = 10x2 -55 + 4x + 10x2 = 0 Solving -55 + 4x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -5.5 + 0.4x + x2 = 0.0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 0.4x + 5.5 + x2 = 0.0 + 5.5 Reorder the terms: -5.5 + 5.5 + 0.4x + x2 = 0.0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 0.4x + x2 = 0.0 + 5.5 0.4x + x2 = 0.0 + 5.5 Combine like terms: 0.0 + 5.5 = 5.5 0.4x + x2 = 5.5 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 5.5 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 5.5 + 0.04 Combine like terms: 5.5 + 0.04 = 5.54 0.04 + 0.4x + x2 = 5.54 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 5.54 Calculate the square root of the right side: 2.353720459 Break this problem into two subproblems by setting (x + 0.2) equal to 2.353720459 and -2.353720459.Subproblem 1
x + 0.2 = 2.353720459 Simplifying x + 0.2 = 2.353720459 Reorder the terms: 0.2 + x = 2.353720459 Solving 0.2 + x = 2.353720459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 2.353720459 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 2.353720459 + -0.2 x = 2.353720459 + -0.2 Combine like terms: 2.353720459 + -0.2 = 2.153720459 x = 2.153720459 Simplifying x = 2.153720459Subproblem 2
x + 0.2 = -2.353720459 Simplifying x + 0.2 = -2.353720459 Reorder the terms: 0.2 + x = -2.353720459 Solving 0.2 + x = -2.353720459 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -2.353720459 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -2.353720459 + -0.2 x = -2.353720459 + -0.2 Combine like terms: -2.353720459 + -0.2 = -2.553720459 x = -2.553720459 Simplifying x = -2.553720459Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.153720459, -2.553720459}
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