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Simplifying 16x2 + 21x = 3 Reorder the terms: 21x + 16x2 = 3 Solving 21x + 16x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + 21x + 16x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + 21x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.1875 + 1.3125x + x2 = 0 Move the constant term to the right: Add '0.1875' to each side of the equation. -0.1875 + 1.3125x + 0.1875 + x2 = 0 + 0.1875 Reorder the terms: -0.1875 + 0.1875 + 1.3125x + x2 = 0 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + 1.3125x + x2 = 0 + 0.1875 1.3125x + x2 = 0 + 0.1875 Combine like terms: 0 + 0.1875 = 0.1875 1.3125x + x2 = 0.1875 The x term is 1.3125x. Take half its coefficient (0.65625). Square it (0.4306640625) and add it to both sides. Add '0.4306640625' to each side of the equation. 1.3125x + 0.4306640625 + x2 = 0.1875 + 0.4306640625 Reorder the terms: 0.4306640625 + 1.3125x + x2 = 0.1875 + 0.4306640625 Combine like terms: 0.1875 + 0.4306640625 = 0.6181640625 0.4306640625 + 1.3125x + x2 = 0.6181640625 Factor a perfect square on the left side: (x + 0.65625)(x + 0.65625) = 0.6181640625 Calculate the square root of the right side: 0.786234102 Break this problem into two subproblems by setting (x + 0.65625) equal to 0.786234102 and -0.786234102.Subproblem 1
x + 0.65625 = 0.786234102 Simplifying x + 0.65625 = 0.786234102 Reorder the terms: 0.65625 + x = 0.786234102 Solving 0.65625 + x = 0.786234102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65625' to each side of the equation. 0.65625 + -0.65625 + x = 0.786234102 + -0.65625 Combine like terms: 0.65625 + -0.65625 = 0.00000 0.00000 + x = 0.786234102 + -0.65625 x = 0.786234102 + -0.65625 Combine like terms: 0.786234102 + -0.65625 = 0.129984102 x = 0.129984102 Simplifying x = 0.129984102Subproblem 2
x + 0.65625 = -0.786234102 Simplifying x + 0.65625 = -0.786234102 Reorder the terms: 0.65625 + x = -0.786234102 Solving 0.65625 + x = -0.786234102 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65625' to each side of the equation. 0.65625 + -0.65625 + x = -0.786234102 + -0.65625 Combine like terms: 0.65625 + -0.65625 = 0.00000 0.00000 + x = -0.786234102 + -0.65625 x = -0.786234102 + -0.65625 Combine like terms: -0.786234102 + -0.65625 = -1.442484102 x = -1.442484102 Simplifying x = -1.442484102Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.129984102, -1.442484102}
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