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Simplifying 3x(2x + -25) + -2x = 5 Reorder the terms: 3x(-25 + 2x) + -2x = 5 (-25 * 3x + 2x * 3x) + -2x = 5 (-75x + 6x2) + -2x = 5 Reorder the terms: -75x + -2x + 6x2 = 5 Combine like terms: -75x + -2x = -77x -77x + 6x2 = 5 Solving -77x + 6x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -77x + 6x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -77x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + -12.83333333x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -12.83333333x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -12.83333333x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -12.83333333x + x2 = 0 + 0.8333333333 -12.83333333x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -12.83333333x + x2 = 0.8333333333 The x term is -12.83333333x. Take half its coefficient (-6.416666665). Square it (41.17361109) and add it to both sides. Add '41.17361109' to each side of the equation. -12.83333333x + 41.17361109 + x2 = 0.8333333333 + 41.17361109 Reorder the terms: 41.17361109 + -12.83333333x + x2 = 0.8333333333 + 41.17361109 Combine like terms: 0.8333333333 + 41.17361109 = 42.0069444233 41.17361109 + -12.83333333x + x2 = 42.0069444233 Factor a perfect square on the left side: (x + -6.416666665)(x + -6.416666665) = 42.0069444233 Calculate the square root of the right side: 6.48127645 Break this problem into two subproblems by setting (x + -6.416666665) equal to 6.48127645 and -6.48127645.Subproblem 1
x + -6.416666665 = 6.48127645 Simplifying x + -6.416666665 = 6.48127645 Reorder the terms: -6.416666665 + x = 6.48127645 Solving -6.416666665 + x = 6.48127645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.416666665' to each side of the equation. -6.416666665 + 6.416666665 + x = 6.48127645 + 6.416666665 Combine like terms: -6.416666665 + 6.416666665 = 0.000000000 0.000000000 + x = 6.48127645 + 6.416666665 x = 6.48127645 + 6.416666665 Combine like terms: 6.48127645 + 6.416666665 = 12.897943115 x = 12.897943115 Simplifying x = 12.897943115Subproblem 2
x + -6.416666665 = -6.48127645 Simplifying x + -6.416666665 = -6.48127645 Reorder the terms: -6.416666665 + x = -6.48127645 Solving -6.416666665 + x = -6.48127645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.416666665' to each side of the equation. -6.416666665 + 6.416666665 + x = -6.48127645 + 6.416666665 Combine like terms: -6.416666665 + 6.416666665 = 0.000000000 0.000000000 + x = -6.48127645 + 6.416666665 x = -6.48127645 + 6.416666665 Combine like terms: -6.48127645 + 6.416666665 = -0.064609785 x = -0.064609785 Simplifying x = -0.064609785Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.897943115, -0.064609785}
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