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Simplifying 8x2 + -4x = 1 Reorder the terms: -4x + 8x2 = 1 Solving -4x + 8x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + -4x + 8x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + -4x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.5x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.5x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.5x + x2 = 0 + 0.125 -0.5x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.5x + x2 = 0.125 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 = 0.125 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.125 + 0.0625 Combine like terms: 0.125 + 0.0625 = 0.1875 0.0625 + -0.5x + x2 = 0.1875 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.1875 Calculate the square root of the right side: 0.433012702 Break this problem into two subproblems by setting (x + -0.25) equal to 0.433012702 and -0.433012702.Subproblem 1
x + -0.25 = 0.433012702 Simplifying x + -0.25 = 0.433012702 Reorder the terms: -0.25 + x = 0.433012702 Solving -0.25 + x = 0.433012702 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 = 0.433012702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.433012702 + 0.25 x = 0.433012702 + 0.25 Combine like terms: 0.433012702 + 0.25 = 0.683012702 x = 0.683012702 Simplifying x = 0.683012702Subproblem 2
x + -0.25 = -0.433012702 Simplifying x + -0.25 = -0.433012702 Reorder the terms: -0.25 + x = -0.433012702 Solving -0.25 + x = -0.433012702 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 = -0.433012702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.433012702 + 0.25 x = -0.433012702 + 0.25 Combine like terms: -0.433012702 + 0.25 = -0.183012702 x = -0.183012702 Simplifying x = -0.183012702Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.683012702, -0.183012702}
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