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Simplifying 25x2 + -8x + -4 = 0 Reorder the terms: -4 + -8x + 25x2 = 0 Solving -4 + -8x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.16 + -0.32x + x2 = 0 Move the constant term to the right: Add '0.16' to each side of the equation. -0.16 + -0.32x + 0.16 + x2 = 0 + 0.16 Reorder the terms: -0.16 + 0.16 + -0.32x + x2 = 0 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + -0.32x + x2 = 0 + 0.16 -0.32x + x2 = 0 + 0.16 Combine like terms: 0 + 0.16 = 0.16 -0.32x + x2 = 0.16 The x term is -0.32x. Take half its coefficient (-0.16). Square it (0.0256) and add it to both sides. Add '0.0256' to each side of the equation. -0.32x + 0.0256 + x2 = 0.16 + 0.0256 Reorder the terms: 0.0256 + -0.32x + x2 = 0.16 + 0.0256 Combine like terms: 0.16 + 0.0256 = 0.1856 0.0256 + -0.32x + x2 = 0.1856 Factor a perfect square on the left side: (x + -0.16)(x + -0.16) = 0.1856 Calculate the square root of the right side: 0.430813185 Break this problem into two subproblems by setting (x + -0.16) equal to 0.430813185 and -0.430813185.Subproblem 1
x + -0.16 = 0.430813185 Simplifying x + -0.16 = 0.430813185 Reorder the terms: -0.16 + x = 0.430813185 Solving -0.16 + x = 0.430813185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.16' to each side of the equation. -0.16 + 0.16 + x = 0.430813185 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + x = 0.430813185 + 0.16 x = 0.430813185 + 0.16 Combine like terms: 0.430813185 + 0.16 = 0.590813185 x = 0.590813185 Simplifying x = 0.590813185Subproblem 2
x + -0.16 = -0.430813185 Simplifying x + -0.16 = -0.430813185 Reorder the terms: -0.16 + x = -0.430813185 Solving -0.16 + x = -0.430813185 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.16' to each side of the equation. -0.16 + 0.16 + x = -0.430813185 + 0.16 Combine like terms: -0.16 + 0.16 = 0.00 0.00 + x = -0.430813185 + 0.16 x = -0.430813185 + 0.16 Combine like terms: -0.430813185 + 0.16 = -0.270813185 x = -0.270813185 Simplifying x = -0.270813185Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.590813185, -0.270813185}
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