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Simplifying -1x2 + 0.5x + 0.47375 = 0 Reorder the terms: 0.47375 + 0.5x + -1x2 = 0 Solving 0.47375 + 0.5x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.47375 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.47375' to each side of the equation. -0.47375 + -0.5x + 0.47375 + x2 = 0 + 0.47375 Reorder the terms: -0.47375 + 0.47375 + -0.5x + x2 = 0 + 0.47375 Combine like terms: -0.47375 + 0.47375 = 0.00000 0.00000 + -0.5x + x2 = 0 + 0.47375 -0.5x + x2 = 0 + 0.47375 Combine like terms: 0 + 0.47375 = 0.47375 -0.5x + x2 = 0.47375 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 = 0.47375 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.47375 + 0.0625 Combine like terms: 0.47375 + 0.0625 = 0.53625 0.0625 + -0.5x + x2 = 0.53625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.53625 Calculate the square root of the right side: 0.732290926 Break this problem into two subproblems by setting (x + -0.25) equal to 0.732290926 and -0.732290926.Subproblem 1
x + -0.25 = 0.732290926 Simplifying x + -0.25 = 0.732290926 Reorder the terms: -0.25 + x = 0.732290926 Solving -0.25 + x = 0.732290926 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 = 0.732290926 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.732290926 + 0.25 x = 0.732290926 + 0.25 Combine like terms: 0.732290926 + 0.25 = 0.982290926 x = 0.982290926 Simplifying x = 0.982290926Subproblem 2
x + -0.25 = -0.732290926 Simplifying x + -0.25 = -0.732290926 Reorder the terms: -0.25 + x = -0.732290926 Solving -0.25 + x = -0.732290926 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 = -0.732290926 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.732290926 + 0.25 x = -0.732290926 + 0.25 Combine like terms: -0.732290926 + 0.25 = -0.482290926 x = -0.482290926 Simplifying x = -0.482290926Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.982290926, -0.482290926}
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