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Simplifying 3 + -4x(25 + -2x) = 16x + x + -300 3 + (25 * -4x + -2x * -4x) = 16x + x + -300 3 + (-100x + 8x2) = 16x + x + -300 Reorder the terms: 3 + -100x + 8x2 = -300 + 16x + x Combine like terms: 16x + x = 17x 3 + -100x + 8x2 = -300 + 17x Solving 3 + -100x + 8x2 = -300 + 17x Solving for variable 'x'. Reorder the terms: 3 + 300 + -100x + -17x + 8x2 = -300 + 17x + 300 + -17x Combine like terms: 3 + 300 = 303 303 + -100x + -17x + 8x2 = -300 + 17x + 300 + -17x Combine like terms: -100x + -17x = -117x 303 + -117x + 8x2 = -300 + 17x + 300 + -17x Reorder the terms: 303 + -117x + 8x2 = -300 + 300 + 17x + -17x Combine like terms: -300 + 300 = 0 303 + -117x + 8x2 = 0 + 17x + -17x 303 + -117x + 8x2 = 17x + -17x Combine like terms: 17x + -17x = 0 303 + -117x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 37.875 + -14.625x + x2 = 0 Move the constant term to the right: Add '-37.875' to each side of the equation. 37.875 + -14.625x + -37.875 + x2 = 0 + -37.875 Reorder the terms: 37.875 + -37.875 + -14.625x + x2 = 0 + -37.875 Combine like terms: 37.875 + -37.875 = 0.000 0.000 + -14.625x + x2 = 0 + -37.875 -14.625x + x2 = 0 + -37.875 Combine like terms: 0 + -37.875 = -37.875 -14.625x + x2 = -37.875 The x term is -14.625x. Take half its coefficient (-7.3125). Square it (53.47265625) and add it to both sides. Add '53.47265625' to each side of the equation. -14.625x + 53.47265625 + x2 = -37.875 + 53.47265625 Reorder the terms: 53.47265625 + -14.625x + x2 = -37.875 + 53.47265625 Combine like terms: -37.875 + 53.47265625 = 15.59765625 53.47265625 + -14.625x + x2 = 15.59765625 Factor a perfect square on the left side: (x + -7.3125)(x + -7.3125) = 15.59765625 Calculate the square root of the right side: 3.949386819 Break this problem into two subproblems by setting (x + -7.3125) equal to 3.949386819 and -3.949386819.Subproblem 1
x + -7.3125 = 3.949386819 Simplifying x + -7.3125 = 3.949386819 Reorder the terms: -7.3125 + x = 3.949386819 Solving -7.3125 + x = 3.949386819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.3125' to each side of the equation. -7.3125 + 7.3125 + x = 3.949386819 + 7.3125 Combine like terms: -7.3125 + 7.3125 = 0.0000 0.0000 + x = 3.949386819 + 7.3125 x = 3.949386819 + 7.3125 Combine like terms: 3.949386819 + 7.3125 = 11.261886819 x = 11.261886819 Simplifying x = 11.261886819Subproblem 2
x + -7.3125 = -3.949386819 Simplifying x + -7.3125 = -3.949386819 Reorder the terms: -7.3125 + x = -3.949386819 Solving -7.3125 + x = -3.949386819 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.3125' to each side of the equation. -7.3125 + 7.3125 + x = -3.949386819 + 7.3125 Combine like terms: -7.3125 + 7.3125 = 0.0000 0.0000 + x = -3.949386819 + 7.3125 x = -3.949386819 + 7.3125 Combine like terms: -3.949386819 + 7.3125 = 3.363113181 x = 3.363113181 Simplifying x = 3.363113181Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.261886819, 3.363113181}
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