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Simplifying 16x + 3.5x2 = 50 Solving 16x + 3.5x2 = 50 Solving for variable 'x'. Reorder the terms: -50 + 16x + 3.5x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -50 + 16x + 3.5x2 = 0 Begin completing the square. Divide all terms by 3.5 the coefficient of the squared term: Divide each side by '3.5'. -14.28571429 + 4.571428571x + x2 = 0 Move the constant term to the right: Add '14.28571429' to each side of the equation. -14.28571429 + 4.571428571x + 14.28571429 + x2 = 0 + 14.28571429 Reorder the terms: -14.28571429 + 14.28571429 + 4.571428571x + x2 = 0 + 14.28571429 Combine like terms: -14.28571429 + 14.28571429 = 0.00000000 0.00000000 + 4.571428571x + x2 = 0 + 14.28571429 4.571428571x + x2 = 0 + 14.28571429 Combine like terms: 0 + 14.28571429 = 14.28571429 4.571428571x + x2 = 14.28571429 The x term is 4.571428571x. Take half its coefficient (2.285714286). Square it (5.224489797) and add it to both sides. Add '5.224489797' to each side of the equation. 4.571428571x + 5.224489797 + x2 = 14.28571429 + 5.224489797 Reorder the terms: 5.224489797 + 4.571428571x + x2 = 14.28571429 + 5.224489797 Combine like terms: 14.28571429 + 5.224489797 = 19.510204087 5.224489797 + 4.571428571x + x2 = 19.510204087 Factor a perfect square on the left side: (x + 2.285714286)(x + 2.285714286) = 19.510204087 Calculate the square root of the right side: 4.417035667 Break this problem into two subproblems by setting (x + 2.285714286) equal to 4.417035667 and -4.417035667.Subproblem 1
x + 2.285714286 = 4.417035667 Simplifying x + 2.285714286 = 4.417035667 Reorder the terms: 2.285714286 + x = 4.417035667 Solving 2.285714286 + x = 4.417035667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.285714286' to each side of the equation. 2.285714286 + -2.285714286 + x = 4.417035667 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + x = 4.417035667 + -2.285714286 x = 4.417035667 + -2.285714286 Combine like terms: 4.417035667 + -2.285714286 = 2.131321381 x = 2.131321381 Simplifying x = 2.131321381Subproblem 2
x + 2.285714286 = -4.417035667 Simplifying x + 2.285714286 = -4.417035667 Reorder the terms: 2.285714286 + x = -4.417035667 Solving 2.285714286 + x = -4.417035667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.285714286' to each side of the equation. 2.285714286 + -2.285714286 + x = -4.417035667 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + x = -4.417035667 + -2.285714286 x = -4.417035667 + -2.285714286 Combine like terms: -4.417035667 + -2.285714286 = -6.702749953 x = -6.702749953 Simplifying x = -6.702749953Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.131321381, -6.702749953}
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