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Simplifying 6x2 + -5x = -2x2 + 25 Reorder the terms: -5x + 6x2 = -2x2 + 25 Reorder the terms: -5x + 6x2 = 25 + -2x2 Solving -5x + 6x2 = 25 + -2x2 Solving for variable 'x'. Reorder the terms: -25 + -5x + 6x2 + 2x2 = 25 + -2x2 + -25 + 2x2 Combine like terms: 6x2 + 2x2 = 8x2 -25 + -5x + 8x2 = 25 + -2x2 + -25 + 2x2 Reorder the terms: -25 + -5x + 8x2 = 25 + -25 + -2x2 + 2x2 Combine like terms: 25 + -25 = 0 -25 + -5x + 8x2 = 0 + -2x2 + 2x2 -25 + -5x + 8x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -25 + -5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -3.125 + -0.625x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + -0.625x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + -0.625x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + -0.625x + x2 = 0 + 3.125 -0.625x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 -0.625x + x2 = 3.125 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 3.125 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 3.125 + 0.09765625 Combine like terms: 3.125 + 0.09765625 = 3.22265625 0.09765625 + -0.625x + x2 = 3.22265625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 3.22265625 Calculate the square root of the right side: 1.795175827 Break this problem into two subproblems by setting (x + -0.3125) equal to 1.795175827 and -1.795175827.Subproblem 1
x + -0.3125 = 1.795175827 Simplifying x + -0.3125 = 1.795175827 Reorder the terms: -0.3125 + x = 1.795175827 Solving -0.3125 + x = 1.795175827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 1.795175827 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 1.795175827 + 0.3125 x = 1.795175827 + 0.3125 Combine like terms: 1.795175827 + 0.3125 = 2.107675827 x = 2.107675827 Simplifying x = 2.107675827Subproblem 2
x + -0.3125 = -1.795175827 Simplifying x + -0.3125 = -1.795175827 Reorder the terms: -0.3125 + x = -1.795175827 Solving -0.3125 + x = -1.795175827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -1.795175827 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -1.795175827 + 0.3125 x = -1.795175827 + 0.3125 Combine like terms: -1.795175827 + 0.3125 = -1.482675827 x = -1.482675827 Simplifying x = -1.482675827Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.107675827, -1.482675827}
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