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Simplifying 25x2 + -24x + -25 = 0 Reorder the terms: -25 + -24x + 25x2 = 0 Solving -25 + -24x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -1 + -0.96x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -0.96x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -0.96x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -0.96x + x2 = 0 + 1 -0.96x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -0.96x + x2 = 1 The x term is -0.96x. Take half its coefficient (-0.48). Square it (0.2304) and add it to both sides. Add '0.2304' to each side of the equation. -0.96x + 0.2304 + x2 = 1 + 0.2304 Reorder the terms: 0.2304 + -0.96x + x2 = 1 + 0.2304 Combine like terms: 1 + 0.2304 = 1.2304 0.2304 + -0.96x + x2 = 1.2304 Factor a perfect square on the left side: (x + -0.48)(x + -0.48) = 1.2304 Calculate the square root of the right side: 1.10923397 Break this problem into two subproblems by setting (x + -0.48) equal to 1.10923397 and -1.10923397.Subproblem 1
x + -0.48 = 1.10923397 Simplifying x + -0.48 = 1.10923397 Reorder the terms: -0.48 + x = 1.10923397 Solving -0.48 + x = 1.10923397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.48' to each side of the equation. -0.48 + 0.48 + x = 1.10923397 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + x = 1.10923397 + 0.48 x = 1.10923397 + 0.48 Combine like terms: 1.10923397 + 0.48 = 1.58923397 x = 1.58923397 Simplifying x = 1.58923397Subproblem 2
x + -0.48 = -1.10923397 Simplifying x + -0.48 = -1.10923397 Reorder the terms: -0.48 + x = -1.10923397 Solving -0.48 + x = -1.10923397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.48' to each side of the equation. -0.48 + 0.48 + x = -1.10923397 + 0.48 Combine like terms: -0.48 + 0.48 = 0.00 0.00 + x = -1.10923397 + 0.48 x = -1.10923397 + 0.48 Combine like terms: -1.10923397 + 0.48 = -0.62923397 x = -0.62923397 Simplifying x = -0.62923397Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.58923397, -0.62923397}
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