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Simplifying (7 + -1x)(3.14159265359 + 2x) = 0 Multiply (7 + -1x) * (3.14159265359 + 2x) (7(3.14159265359 + 2x) + -1x * (3.14159265359 + 2x)) = 0 ((3.14159265359 * 7 + 2x * 7) + -1x * (3.14159265359 + 2x)) = 0 ((21.99114858 + 14x) + -1x * (3.14159265359 + 2x)) = 0 (21.99114858 + 14x + (3.14159265359 * -1x + 2x * -1x)) = 0 (21.99114858 + 14x + (-3.141592654x + -2x2)) = 0 Combine like terms: 14x + -3.141592654x = 10.858407346x (21.99114858 + 10.858407346x + -2x2) = 0 Solving 21.99114858 + 10.858407346x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -10.99557429 + -5.429203673x + x2 = 0 Move the constant term to the right: Add '10.99557429' to each side of the equation. -10.99557429 + -5.429203673x + 10.99557429 + x2 = 0 + 10.99557429 Reorder the terms: -10.99557429 + 10.99557429 + -5.429203673x + x2 = 0 + 10.99557429 Combine like terms: -10.99557429 + 10.99557429 = 0.00000000 0.00000000 + -5.429203673x + x2 = 0 + 10.99557429 -5.429203673x + x2 = 0 + 10.99557429 Combine like terms: 0 + 10.99557429 = 10.99557429 -5.429203673x + x2 = 10.99557429 The x term is -5.429203673x. Take half its coefficient (-2.714601837). Square it (7.369063133) and add it to both sides. Add '7.369063133' to each side of the equation. -5.429203673x + 7.369063133 + x2 = 10.99557429 + 7.369063133 Reorder the terms: 7.369063133 + -5.429203673x + x2 = 10.99557429 + 7.369063133 Combine like terms: 10.99557429 + 7.369063133 = 18.364637423 7.369063133 + -5.429203673x + x2 = 18.364637423 Factor a perfect square on the left side: (x + -2.714601837)(x + -2.714601837) = 18.364637423 Calculate the square root of the right side: 4.285398164 Break this problem into two subproblems by setting (x + -2.714601837) equal to 4.285398164 and -4.285398164.Subproblem 1
x + -2.714601837 = 4.285398164 Simplifying x + -2.714601837 = 4.285398164 Reorder the terms: -2.714601837 + x = 4.285398164 Solving -2.714601837 + x = 4.285398164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.714601837' to each side of the equation. -2.714601837 + 2.714601837 + x = 4.285398164 + 2.714601837 Combine like terms: -2.714601837 + 2.714601837 = 0.000000000 0.000000000 + x = 4.285398164 + 2.714601837 x = 4.285398164 + 2.714601837 Combine like terms: 4.285398164 + 2.714601837 = 7.000000001 x = 7.000000001 Simplifying x = 7.000000001Subproblem 2
x + -2.714601837 = -4.285398164 Simplifying x + -2.714601837 = -4.285398164 Reorder the terms: -2.714601837 + x = -4.285398164 Solving -2.714601837 + x = -4.285398164 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.714601837' to each side of the equation. -2.714601837 + 2.714601837 + x = -4.285398164 + 2.714601837 Combine like terms: -2.714601837 + 2.714601837 = 0.000000000 0.000000000 + x = -4.285398164 + 2.714601837 x = -4.285398164 + 2.714601837 Combine like terms: -4.285398164 + 2.714601837 = -1.570796327 x = -1.570796327 Simplifying x = -1.570796327Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.000000001, -1.570796327}
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