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Simplifying 49x2 + 168x + 144 = 99 Reorder the terms: 144 + 168x + 49x2 = 99 Solving 144 + 168x + 49x2 = 99 Solving for variable 'x'. Reorder the terms: 144 + -99 + 168x + 49x2 = 99 + -99 Combine like terms: 144 + -99 = 45 45 + 168x + 49x2 = 99 + -99 Combine like terms: 99 + -99 = 0 45 + 168x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.9183673469 + 3.428571429x + x2 = 0 Move the constant term to the right: Add '-0.9183673469' to each side of the equation. 0.9183673469 + 3.428571429x + -0.9183673469 + x2 = 0 + -0.9183673469 Reorder the terms: 0.9183673469 + -0.9183673469 + 3.428571429x + x2 = 0 + -0.9183673469 Combine like terms: 0.9183673469 + -0.9183673469 = 0.0000000000 0.0000000000 + 3.428571429x + x2 = 0 + -0.9183673469 3.428571429x + x2 = 0 + -0.9183673469 Combine like terms: 0 + -0.9183673469 = -0.9183673469 3.428571429x + x2 = -0.9183673469 The x term is 3.428571429x. Take half its coefficient (1.714285715). Square it (2.938775513) and add it to both sides. Add '2.938775513' to each side of the equation. 3.428571429x + 2.938775513 + x2 = -0.9183673469 + 2.938775513 Reorder the terms: 2.938775513 + 3.428571429x + x2 = -0.9183673469 + 2.938775513 Combine like terms: -0.9183673469 + 2.938775513 = 2.0204081661 2.938775513 + 3.428571429x + x2 = 2.0204081661 Factor a perfect square on the left side: (x + 1.714285715)(x + 1.714285715) = 2.0204081661 Calculate the square root of the right side: 1.421410625 Break this problem into two subproblems by setting (x + 1.714285715) equal to 1.421410625 and -1.421410625.Subproblem 1
x + 1.714285715 = 1.421410625 Simplifying x + 1.714285715 = 1.421410625 Reorder the terms: 1.714285715 + x = 1.421410625 Solving 1.714285715 + x = 1.421410625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.714285715' to each side of the equation. 1.714285715 + -1.714285715 + x = 1.421410625 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = 1.421410625 + -1.714285715 x = 1.421410625 + -1.714285715 Combine like terms: 1.421410625 + -1.714285715 = -0.29287509 x = -0.29287509 Simplifying x = -0.29287509Subproblem 2
x + 1.714285715 = -1.421410625 Simplifying x + 1.714285715 = -1.421410625 Reorder the terms: 1.714285715 + x = -1.421410625 Solving 1.714285715 + x = -1.421410625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.714285715' to each side of the equation. 1.714285715 + -1.714285715 + x = -1.421410625 + -1.714285715 Combine like terms: 1.714285715 + -1.714285715 = 0.000000000 0.000000000 + x = -1.421410625 + -1.714285715 x = -1.421410625 + -1.714285715 Combine like terms: -1.421410625 + -1.714285715 = -3.13569634 x = -3.13569634 Simplifying x = -3.13569634Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.29287509, -3.13569634}
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