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Simplifying -5x + (3x)(3x) + -3x + 100 + -125 = 0 Remove parenthesis around (3x) -5x + 3x(3x) + -3x + 100 + -125 = 0 Remove parenthesis around (3x) -5x + 3x * 3x + -3x + 100 + -125 = 0 Reorder the terms for easier multiplication: -5x + 3 * 3x * x + -3x + 100 + -125 = 0 Multiply 3 * 3 -5x + 9x * x + -3x + 100 + -125 = 0 Multiply x * x -5x + 9x2 + -3x + 100 + -125 = 0 Reorder the terms: 100 + -125 + -5x + -3x + 9x2 = 0 Combine like terms: 100 + -125 = -25 -25 + -5x + -3x + 9x2 = 0 Combine like terms: -5x + -3x = -8x -25 + -8x + 9x2 = 0 Solving -25 + -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'. -2.777777778 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '2.777777778' to each side of the equation. -2.777777778 + -0.8888888889x + 2.777777778 + x2 = 0 + 2.777777778 Reorder the terms: -2.777777778 + 2.777777778 + -0.8888888889x + x2 = 0 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + -0.8888888889x + x2 = 0 + 2.777777778 -0.8888888889x + x2 = 0 + 2.777777778 Combine like terms: 0 + 2.777777778 = 2.777777778 -0.8888888889x + x2 = 2.777777778 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 = 2.777777778 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 2.777777778 + 0.1975308642 Combine like terms: 2.777777778 + 0.1975308642 = 2.9753086422 0.1975308642 + -0.8888888889x + x2 = 2.9753086422 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 2.9753086422 Calculate the square root of the right side: 1.7249083 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 1.7249083 and -1.7249083.Subproblem 1
x + -0.4444444445 = 1.7249083 Simplifying x + -0.4444444445 = 1.7249083 Reorder the terms: -0.4444444445 + x = 1.7249083 Solving -0.4444444445 + x = 1.7249083 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 = 1.7249083 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 1.7249083 + 0.4444444445 x = 1.7249083 + 0.4444444445 Combine like terms: 1.7249083 + 0.4444444445 = 2.1693527445 x = 2.1693527445 Simplifying x = 2.1693527445Subproblem 2
x + -0.4444444445 = -1.7249083 Simplifying x + -0.4444444445 = -1.7249083 Reorder the terms: -0.4444444445 + x = -1.7249083 Solving -0.4444444445 + x = -1.7249083 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 = -1.7249083 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -1.7249083 + 0.4444444445 x = -1.7249083 + 0.4444444445 Combine like terms: -1.7249083 + 0.4444444445 = -1.2804638555 x = -1.2804638555 Simplifying x = -1.2804638555Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1693527445, -1.2804638555}
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