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Simplifying 16x + -8x2 + -3.14159265359 = 0 Reorder the terms: -3.14159265359 + 16x + -8x2 = 0 Solving -3.14159265359 + 16x + -8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 0.3926990817 + -2x + x2 = 0 Move the constant term to the right: Add '-0.3926990817' to each side of the equation. 0.3926990817 + -2x + -0.3926990817 + x2 = 0 + -0.3926990817 Reorder the terms: 0.3926990817 + -0.3926990817 + -2x + x2 = 0 + -0.3926990817 Combine like terms: 0.3926990817 + -0.3926990817 = 0.0000000000 0.0000000000 + -2x + x2 = 0 + -0.3926990817 -2x + x2 = 0 + -0.3926990817 Combine like terms: 0 + -0.3926990817 = -0.3926990817 -2x + x2 = -0.3926990817 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -0.3926990817 + 1 Reorder the terms: 1 + -2x + x2 = -0.3926990817 + 1 Combine like terms: -0.3926990817 + 1 = 0.6073009183 1 + -2x + x2 = 0.6073009183 Factor a perfect square on the left side: (x + -1)(x + -1) = 0.6073009183 Calculate the square root of the right side: 0.779295142 Break this problem into two subproblems by setting (x + -1) equal to 0.779295142 and -0.779295142.Subproblem 1
x + -1 = 0.779295142 Simplifying x + -1 = 0.779295142 Reorder the terms: -1 + x = 0.779295142 Solving -1 + x = 0.779295142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.779295142 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.779295142 + 1 x = 0.779295142 + 1 Combine like terms: 0.779295142 + 1 = 1.779295142 x = 1.779295142 Simplifying x = 1.779295142Subproblem 2
x + -1 = -0.779295142 Simplifying x + -1 = -0.779295142 Reorder the terms: -1 + x = -0.779295142 Solving -1 + x = -0.779295142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.779295142 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.779295142 + 1 x = -0.779295142 + 1 Combine like terms: -0.779295142 + 1 = 0.220704858 x = 0.220704858 Simplifying x = 0.220704858Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.779295142, 0.220704858}
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