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Simplifying 16x2 + -151.2x + 282.24 = 0 Reorder the terms: 282.24 + -151.2x + 16x2 = 0 Solving 282.24 + -151.2x + 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'. 17.64 + -9.45x + x2 = 0 Move the constant term to the right: Add '-17.64' to each side of the equation. 17.64 + -9.45x + -17.64 + x2 = 0 + -17.64 Reorder the terms: 17.64 + -17.64 + -9.45x + x2 = 0 + -17.64 Combine like terms: 17.64 + -17.64 = 0.00 0.00 + -9.45x + x2 = 0 + -17.64 -9.45x + x2 = 0 + -17.64 Combine like terms: 0 + -17.64 = -17.64 -9.45x + x2 = -17.64 The x term is -9.45x. Take half its coefficient (-4.725). Square it (22.325625) and add it to both sides. Add '22.325625' to each side of the equation. -9.45x + 22.325625 + x2 = -17.64 + 22.325625 Reorder the terms: 22.325625 + -9.45x + x2 = -17.64 + 22.325625 Combine like terms: -17.64 + 22.325625 = 4.685625 22.325625 + -9.45x + x2 = 4.685625 Factor a perfect square on the left side: (x + -4.725)(x + -4.725) = 4.685625 Calculate the square root of the right side: 2.164630453 Break this problem into two subproblems by setting (x + -4.725) equal to 2.164630453 and -2.164630453.Subproblem 1
x + -4.725 = 2.164630453 Simplifying x + -4.725 = 2.164630453 Reorder the terms: -4.725 + x = 2.164630453 Solving -4.725 + x = 2.164630453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.725' to each side of the equation. -4.725 + 4.725 + x = 2.164630453 + 4.725 Combine like terms: -4.725 + 4.725 = 0.000 0.000 + x = 2.164630453 + 4.725 x = 2.164630453 + 4.725 Combine like terms: 2.164630453 + 4.725 = 6.889630453 x = 6.889630453 Simplifying x = 6.889630453Subproblem 2
x + -4.725 = -2.164630453 Simplifying x + -4.725 = -2.164630453 Reorder the terms: -4.725 + x = -2.164630453 Solving -4.725 + x = -2.164630453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.725' to each side of the equation. -4.725 + 4.725 + x = -2.164630453 + 4.725 Combine like terms: -4.725 + 4.725 = 0.000 0.000 + x = -2.164630453 + 4.725 x = -2.164630453 + 4.725 Combine like terms: -2.164630453 + 4.725 = 2.560369547 x = 2.560369547 Simplifying x = 2.560369547Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.889630453, 2.560369547}
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