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Simplifying 2x2 + -25x + -9.3 = 0 Reorder the terms: -9.3 + -25x + 2x2 = 0 Solving -9.3 + -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'. -4.65 + -12.5x + x2 = 0 Move the constant term to the right: Add '4.65' to each side of the equation. -4.65 + -12.5x + 4.65 + x2 = 0 + 4.65 Reorder the terms: -4.65 + 4.65 + -12.5x + x2 = 0 + 4.65 Combine like terms: -4.65 + 4.65 = 0.00 0.00 + -12.5x + x2 = 0 + 4.65 -12.5x + x2 = 0 + 4.65 Combine like terms: 0 + 4.65 = 4.65 -12.5x + x2 = 4.65 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 = 4.65 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 4.65 + 39.0625 Combine like terms: 4.65 + 39.0625 = 43.7125 39.0625 + -12.5x + x2 = 43.7125 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 43.7125 Calculate the square root of the right side: 6.611542936 Break this problem into two subproblems by setting (x + -6.25) equal to 6.611542936 and -6.611542936.Subproblem 1
x + -6.25 = 6.611542936 Simplifying x + -6.25 = 6.611542936 Reorder the terms: -6.25 + x = 6.611542936 Solving -6.25 + x = 6.611542936 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 = 6.611542936 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 6.611542936 + 6.25 x = 6.611542936 + 6.25 Combine like terms: 6.611542936 + 6.25 = 12.861542936 x = 12.861542936 Simplifying x = 12.861542936Subproblem 2
x + -6.25 = -6.611542936 Simplifying x + -6.25 = -6.611542936 Reorder the terms: -6.25 + x = -6.611542936 Solving -6.25 + x = -6.611542936 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 = -6.611542936 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -6.611542936 + 6.25 x = -6.611542936 + 6.25 Combine like terms: -6.611542936 + 6.25 = -0.361542936 x = -0.361542936 Simplifying x = -0.361542936Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.861542936, -0.361542936}
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