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Simplifying 2X2 + 3X + -25 = 0 Reorder the terms: -25 + 3X + 2X2 = 0 Solving -25 + 3X + 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'. -12.5 + 1.5X + X2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 1.5X + 12.5 + X2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 1.5X + X2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 1.5X + X2 = 0 + 12.5 1.5X + X2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 1.5X + X2 = 12.5 The X term is 1.5X. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5X + 0.5625 + X2 = 12.5 + 0.5625 Reorder the terms: 0.5625 + 1.5X + X2 = 12.5 + 0.5625 Combine like terms: 12.5 + 0.5625 = 13.0625 0.5625 + 1.5X + X2 = 13.0625 Factor a perfect square on the left side: (X + 0.75)(X + 0.75) = 13.0625 Calculate the square root of the right side: 3.614208074 Break this problem into two subproblems by setting (X + 0.75) equal to 3.614208074 and -3.614208074.Subproblem 1
X + 0.75 = 3.614208074 Simplifying X + 0.75 = 3.614208074 Reorder the terms: 0.75 + X = 3.614208074 Solving 0.75 + X = 3.614208074 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + X = 3.614208074 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = 3.614208074 + -0.75 X = 3.614208074 + -0.75 Combine like terms: 3.614208074 + -0.75 = 2.864208074 X = 2.864208074 Simplifying X = 2.864208074Subproblem 2
X + 0.75 = -3.614208074 Simplifying X + 0.75 = -3.614208074 Reorder the terms: 0.75 + X = -3.614208074 Solving 0.75 + X = -3.614208074 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + X = -3.614208074 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + X = -3.614208074 + -0.75 X = -3.614208074 + -0.75 Combine like terms: -3.614208074 + -0.75 = -4.364208074 X = -4.364208074 Simplifying X = -4.364208074Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.864208074, -4.364208074}
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