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Simplifying (7x2 + -6x + 22) + (9x2 + 9x + -79) = 0 Reorder the terms: (22 + -6x + 7x2) + (9x2 + 9x + -79) = 0 Remove parenthesis around (22 + -6x + 7x2) 22 + -6x + 7x2 + (9x2 + 9x + -79) = 0 Reorder the terms: 22 + -6x + 7x2 + (-79 + 9x + 9x2) = 0 Remove parenthesis around (-79 + 9x + 9x2) 22 + -6x + 7x2 + -79 + 9x + 9x2 = 0 Reorder the terms: 22 + -79 + -6x + 9x + 7x2 + 9x2 = 0 Combine like terms: 22 + -79 = -57 -57 + -6x + 9x + 7x2 + 9x2 = 0 Combine like terms: -6x + 9x = 3x -57 + 3x + 7x2 + 9x2 = 0 Combine like terms: 7x2 + 9x2 = 16x2 -57 + 3x + 16x2 = 0 Solving -57 + 3x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -3.5625 + 0.1875x + x2 = 0 Move the constant term to the right: Add '3.5625' to each side of the equation. -3.5625 + 0.1875x + 3.5625 + x2 = 0 + 3.5625 Reorder the terms: -3.5625 + 3.5625 + 0.1875x + x2 = 0 + 3.5625 Combine like terms: -3.5625 + 3.5625 = 0.0000 0.0000 + 0.1875x + x2 = 0 + 3.5625 0.1875x + x2 = 0 + 3.5625 Combine like terms: 0 + 3.5625 = 3.5625 0.1875x + x2 = 3.5625 The x term is 0.1875x. Take half its coefficient (0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. 0.1875x + 0.0087890625 + x2 = 3.5625 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = 3.5625 + 0.0087890625 Combine like terms: 3.5625 + 0.0087890625 = 3.5712890625 0.0087890625 + 0.1875x + x2 = 3.5712890625 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = 3.5712890625 Calculate the square root of the right side: 1.889785454 Break this problem into two subproblems by setting (x + 0.09375) equal to 1.889785454 and -1.889785454.Subproblem 1
x + 0.09375 = 1.889785454 Simplifying x + 0.09375 = 1.889785454 Reorder the terms: 0.09375 + x = 1.889785454 Solving 0.09375 + x = 1.889785454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = 1.889785454 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 1.889785454 + -0.09375 x = 1.889785454 + -0.09375 Combine like terms: 1.889785454 + -0.09375 = 1.796035454 x = 1.796035454 Simplifying x = 1.796035454Subproblem 2
x + 0.09375 = -1.889785454 Simplifying x + 0.09375 = -1.889785454 Reorder the terms: 0.09375 + x = -1.889785454 Solving 0.09375 + x = -1.889785454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = -1.889785454 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -1.889785454 + -0.09375 x = -1.889785454 + -0.09375 Combine like terms: -1.889785454 + -0.09375 = -1.983535454 x = -1.983535454 Simplifying x = -1.983535454Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.796035454, -1.983535454}
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