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Simplifying 2x2 + 25x + -6.7 = 0 Reorder the terms: -6.7 + 25x + 2x2 = 0 Solving -6.7 + 25x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.35 + 12.5x + x2 = 0 Move the constant term to the right: Add '3.35' to each side of the equation. -3.35 + 12.5x + 3.35 + x2 = 0 + 3.35 Reorder the terms: -3.35 + 3.35 + 12.5x + x2 = 0 + 3.35 Combine like terms: -3.35 + 3.35 = 0.00 0.00 + 12.5x + x2 = 0 + 3.35 12.5x + x2 = 0 + 3.35 Combine like terms: 0 + 3.35 = 3.35 12.5x + x2 = 3.35 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 = 3.35 + 39.0625 Reorder the terms: 39.0625 + 12.5x + x2 = 3.35 + 39.0625 Combine like terms: 3.35 + 39.0625 = 42.4125 39.0625 + 12.5x + x2 = 42.4125 Factor a perfect square on the left side: (x + 6.25)(x + 6.25) = 42.4125 Calculate the square root of the right side: 6.512488004 Break this problem into two subproblems by setting (x + 6.25) equal to 6.512488004 and -6.512488004.Subproblem 1
x + 6.25 = 6.512488004 Simplifying x + 6.25 = 6.512488004 Reorder the terms: 6.25 + x = 6.512488004 Solving 6.25 + x = 6.512488004 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 = 6.512488004 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = 6.512488004 + -6.25 x = 6.512488004 + -6.25 Combine like terms: 6.512488004 + -6.25 = 0.262488004 x = 0.262488004 Simplifying x = 0.262488004Subproblem 2
x + 6.25 = -6.512488004 Simplifying x + 6.25 = -6.512488004 Reorder the terms: 6.25 + x = -6.512488004 Solving 6.25 + x = -6.512488004 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 = -6.512488004 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + x = -6.512488004 + -6.25 x = -6.512488004 + -6.25 Combine like terms: -6.512488004 + -6.25 = -12.762488004 x = -12.762488004 Simplifying x = -12.762488004Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.262488004, -12.762488004}
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