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Simplifying -16x2 + 99x + 122 = 0 Reorder the terms: 122 + 99x + -16x2 = 0 Solving 122 + 99x + -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'. -7.625 + -6.1875x + x2 = 0 Move the constant term to the right: Add '7.625' to each side of the equation. -7.625 + -6.1875x + 7.625 + x2 = 0 + 7.625 Reorder the terms: -7.625 + 7.625 + -6.1875x + x2 = 0 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + -6.1875x + x2 = 0 + 7.625 -6.1875x + x2 = 0 + 7.625 Combine like terms: 0 + 7.625 = 7.625 -6.1875x + x2 = 7.625 The x term is -6.1875x. Take half its coefficient (-3.09375). Square it (9.571289063) and add it to both sides. Add '9.571289063' to each side of the equation. -6.1875x + 9.571289063 + x2 = 7.625 + 9.571289063 Reorder the terms: 9.571289063 + -6.1875x + x2 = 7.625 + 9.571289063 Combine like terms: 7.625 + 9.571289063 = 17.196289063 9.571289063 + -6.1875x + x2 = 17.196289063 Factor a perfect square on the left side: (x + -3.09375)(x + -3.09375) = 17.196289063 Calculate the square root of the right side: 4.146840853 Break this problem into two subproblems by setting (x + -3.09375) equal to 4.146840853 and -4.146840853.Subproblem 1
x + -3.09375 = 4.146840853 Simplifying x + -3.09375 = 4.146840853 Reorder the terms: -3.09375 + x = 4.146840853 Solving -3.09375 + x = 4.146840853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.09375' to each side of the equation. -3.09375 + 3.09375 + x = 4.146840853 + 3.09375 Combine like terms: -3.09375 + 3.09375 = 0.00000 0.00000 + x = 4.146840853 + 3.09375 x = 4.146840853 + 3.09375 Combine like terms: 4.146840853 + 3.09375 = 7.240590853 x = 7.240590853 Simplifying x = 7.240590853Subproblem 2
x + -3.09375 = -4.146840853 Simplifying x + -3.09375 = -4.146840853 Reorder the terms: -3.09375 + x = -4.146840853 Solving -3.09375 + x = -4.146840853 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.09375' to each side of the equation. -3.09375 + 3.09375 + x = -4.146840853 + 3.09375 Combine like terms: -3.09375 + 3.09375 = 0.00000 0.00000 + x = -4.146840853 + 3.09375 x = -4.146840853 + 3.09375 Combine like terms: -4.146840853 + 3.09375 = -1.053090853 x = -1.053090853 Simplifying x = -1.053090853Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.240590853, -1.053090853}
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