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Simplifying 8x2 + -100x + 75 = 0 Reorder the terms: 75 + -100x + 8x2 = 0 Solving 75 + -100x + 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'. 9.375 + -12.5x + x2 = 0 Move the constant term to the right: Add '-9.375' to each side of the equation. 9.375 + -12.5x + -9.375 + x2 = 0 + -9.375 Reorder the terms: 9.375 + -9.375 + -12.5x + x2 = 0 + -9.375 Combine like terms: 9.375 + -9.375 = 0.000 0.000 + -12.5x + x2 = 0 + -9.375 -12.5x + x2 = 0 + -9.375 Combine like terms: 0 + -9.375 = -9.375 -12.5x + x2 = -9.375 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = -9.375 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = -9.375 + 39.0625 Combine like terms: -9.375 + 39.0625 = 29.6875 39.0625 + -12.5x + x2 = 29.6875 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 29.6875 Calculate the square root of the right side: 5.448623679 Break this problem into two subproblems by setting (x + -6.25) equal to 5.448623679 and -5.448623679.Subproblem 1
x + -6.25 = 5.448623679 Simplifying x + -6.25 = 5.448623679 Reorder the terms: -6.25 + x = 5.448623679 Solving -6.25 + x = 5.448623679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 5.448623679 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 5.448623679 + 6.25 x = 5.448623679 + 6.25 Combine like terms: 5.448623679 + 6.25 = 11.698623679 x = 11.698623679 Simplifying x = 11.698623679Subproblem 2
x + -6.25 = -5.448623679 Simplifying x + -6.25 = -5.448623679 Reorder the terms: -6.25 + x = -5.448623679 Solving -6.25 + x = -5.448623679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -5.448623679 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -5.448623679 + 6.25 x = -5.448623679 + 6.25 Combine like terms: -5.448623679 + 6.25 = 0.801376321 x = 0.801376321 Simplifying x = 0.801376321Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.698623679, 0.801376321}
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