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Simplifying 4x2 + -4x = 25 Reorder the terms: -4x + 4x2 = 25 Solving -4x + 4x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -4x + 4x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -1x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -1x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -1x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -1x + x2 = 0 + 6.25 -1x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -1x + x2 = 6.25 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 6.25 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 6.25 + 0.25 Combine like terms: 6.25 + 0.25 = 6.5 0.25 + -1x + x2 = 6.5 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 6.5 Calculate the square root of the right side: 2.549509757 Break this problem into two subproblems by setting (x + -0.5) equal to 2.549509757 and -2.549509757.Subproblem 1
x + -0.5 = 2.549509757 Simplifying x + -0.5 = 2.549509757 Reorder the terms: -0.5 + x = 2.549509757 Solving -0.5 + x = 2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.549509757 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.549509757 + 0.5 x = 2.549509757 + 0.5 Combine like terms: 2.549509757 + 0.5 = 3.049509757 x = 3.049509757 Simplifying x = 3.049509757Subproblem 2
x + -0.5 = -2.549509757 Simplifying x + -0.5 = -2.549509757 Reorder the terms: -0.5 + x = -2.549509757 Solving -0.5 + x = -2.549509757 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.549509757 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.549509757 + 0.5 x = -2.549509757 + 0.5 Combine like terms: -2.549509757 + 0.5 = -2.049509757 x = -2.049509757 Simplifying x = -2.049509757Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.049509757, -2.049509757}
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