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Simplifying -8x2 + 4x + 3 = 0 Reorder the terms: 3 + 4x + -8x2 = 0 Solving 3 + 4x + -8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -0.5x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -0.5x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -0.5x + x2 = 0 + 0.375 -0.5x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -0.5x + x2 = 0.375 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.375 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.375 + 0.0625 Combine like terms: 0.375 + 0.0625 = 0.4375 0.0625 + -0.5x + x2 = 0.4375 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.4375 Calculate the square root of the right side: 0.661437828 Break this problem into two subproblems by setting (x + -0.25) equal to 0.661437828 and -0.661437828.Subproblem 1
x + -0.25 = 0.661437828 Simplifying x + -0.25 = 0.661437828 Reorder the terms: -0.25 + x = 0.661437828 Solving -0.25 + x = 0.661437828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.661437828 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.661437828 + 0.25 x = 0.661437828 + 0.25 Combine like terms: 0.661437828 + 0.25 = 0.911437828 x = 0.911437828 Simplifying x = 0.911437828Subproblem 2
x + -0.25 = -0.661437828 Simplifying x + -0.25 = -0.661437828 Reorder the terms: -0.25 + x = -0.661437828 Solving -0.25 + x = -0.661437828 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.661437828 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.661437828 + 0.25 x = -0.661437828 + 0.25 Combine like terms: -0.661437828 + 0.25 = -0.411437828 x = -0.411437828 Simplifying x = -0.411437828Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.911437828, -0.411437828}
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