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Simplifying 3x(3x) + 8x + -16 = 0 Remove parenthesis around (3x) 3x * 3x + 8x + -16 = 0 Reorder the terms for easier multiplication: 3 * 3x * x + 8x + -16 = 0 Multiply 3 * 3 9x * x + 8x + -16 = 0 Multiply x * x 9x2 + 8x + -16 = 0 Reorder the terms: -16 + 8x + 9x2 = 0 Solving -16 + 8x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.777777778 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '1.777777778' to each side of the equation. -1.777777778 + 0.8888888889x + 1.777777778 + x2 = 0 + 1.777777778 Reorder the terms: -1.777777778 + 1.777777778 + 0.8888888889x + x2 = 0 + 1.777777778 Combine like terms: -1.777777778 + 1.777777778 = 0.000000000 0.000000000 + 0.8888888889x + x2 = 0 + 1.777777778 0.8888888889x + x2 = 0 + 1.777777778 Combine like terms: 0 + 1.777777778 = 1.777777778 0.8888888889x + x2 = 1.777777778 The x term is 0.8888888889x. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x + 0.1975308642 + x2 = 1.777777778 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = 1.777777778 + 0.1975308642 Combine like terms: 1.777777778 + 0.1975308642 = 1.9753086422 0.1975308642 + 0.8888888889x + x2 = 1.9753086422 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 1.9753086422 Calculate the square root of the right side: 1.405456738 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 1.405456738 and -1.405456738.Subproblem 1
x + 0.4444444445 = 1.405456738 Simplifying x + 0.4444444445 = 1.405456738 Reorder the terms: 0.4444444445 + x = 1.405456738 Solving 0.4444444445 + x = 1.405456738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = 1.405456738 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 1.405456738 + -0.4444444445 x = 1.405456738 + -0.4444444445 Combine like terms: 1.405456738 + -0.4444444445 = 0.9610122935 x = 0.9610122935 Simplifying x = 0.9610122935Subproblem 2
x + 0.4444444445 = -1.405456738 Simplifying x + 0.4444444445 = -1.405456738 Reorder the terms: 0.4444444445 + x = -1.405456738 Solving 0.4444444445 + x = -1.405456738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = -1.405456738 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -1.405456738 + -0.4444444445 x = -1.405456738 + -0.4444444445 Combine like terms: -1.405456738 + -0.4444444445 = -1.8499011825 x = -1.8499011825 Simplifying x = -1.8499011825Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9610122935, -1.8499011825}
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