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Simplifying 8x2 = 7 + -5x Solving 8x2 = 7 + -5x Solving for variable 'x'. Reorder the terms: -7 + 5x + 8x2 = 7 + -5x + -7 + 5x Reorder the terms: -7 + 5x + 8x2 = 7 + -7 + -5x + 5x Combine like terms: 7 + -7 = 0 -7 + 5x + 8x2 = 0 + -5x + 5x -7 + 5x + 8x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -7 + 5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + 0.625x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 0.625x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 0.625x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 0.625x + x2 = 0 + 0.875 0.625x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 0.625x + x2 = 0.875 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 = 0.875 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x + x2 = 0.875 + 0.09765625 Combine like terms: 0.875 + 0.09765625 = 0.97265625 0.09765625 + 0.625x + x2 = 0.97265625 Factor a perfect square on the left side: (x + 0.3125)(x + 0.3125) = 0.97265625 Calculate the square root of the right side: 0.986233365 Break this problem into two subproblems by setting (x + 0.3125) equal to 0.986233365 and -0.986233365.Subproblem 1
x + 0.3125 = 0.986233365 Simplifying x + 0.3125 = 0.986233365 Reorder the terms: 0.3125 + x = 0.986233365 Solving 0.3125 + x = 0.986233365 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 = 0.986233365 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = 0.986233365 + -0.3125 x = 0.986233365 + -0.3125 Combine like terms: 0.986233365 + -0.3125 = 0.673733365 x = 0.673733365 Simplifying x = 0.673733365Subproblem 2
x + 0.3125 = -0.986233365 Simplifying x + 0.3125 = -0.986233365 Reorder the terms: 0.3125 + x = -0.986233365 Solving 0.3125 + x = -0.986233365 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 = -0.986233365 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x = -0.986233365 + -0.3125 x = -0.986233365 + -0.3125 Combine like terms: -0.986233365 + -0.3125 = -1.298733365 x = -1.298733365 Simplifying x = -1.298733365Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.673733365, -1.298733365}
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