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Simplifying 2x2 + 3x = 25 Reorder the terms: 3x + 2x2 = 25 Solving 3x + 2x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + 3x + 2x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 3x + 2x2 = 0 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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