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Simplifying 2x2 + -7x + -20 = x2 + -10x + 25 Reorder the terms: -20 + -7x + 2x2 = x2 + -10x + 25 Reorder the terms: -20 + -7x + 2x2 = 25 + -10x + x2 Solving -20 + -7x + 2x2 = 25 + -10x + x2 Solving for variable 'x'. Reorder the terms: -20 + -25 + -7x + 10x + 2x2 + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2 Combine like terms: -20 + -25 = -45 -45 + -7x + 10x + 2x2 + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2 Combine like terms: -7x + 10x = 3x -45 + 3x + 2x2 + -1x2 = 25 + -10x + x2 + -25 + 10x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -45 + 3x + 1x2 = 25 + -10x + x2 + -25 + 10x + -1x2 Reorder the terms: -45 + 3x + 1x2 = 25 + -25 + -10x + 10x + x2 + -1x2 Combine like terms: 25 + -25 = 0 -45 + 3x + 1x2 = 0 + -10x + 10x + x2 + -1x2 -45 + 3x + 1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 -45 + 3x + 1x2 = 0 + x2 + -1x2 -45 + 3x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -45 + 3x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 3x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 3x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 3x + x2 = 0 + 45 3x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 3x + x2 = 45 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 45 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 45 + 2.25 Combine like terms: 45 + 2.25 = 47.25 2.25 + 3x + x2 = 47.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (x + 1.5) equal to 6.873863542 and -6.873863542.Subproblem 1
x + 1.5 = 6.873863542 Simplifying x + 1.5 = 6.873863542 Reorder the terms: 1.5 + x = 6.873863542 Solving 1.5 + x = 6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 6.873863542 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.873863542 + -1.5 x = 6.873863542 + -1.5 Combine like terms: 6.873863542 + -1.5 = 5.373863542 x = 5.373863542 Simplifying x = 5.373863542Subproblem 2
x + 1.5 = -6.873863542 Simplifying x + 1.5 = -6.873863542 Reorder the terms: 1.5 + x = -6.873863542 Solving 1.5 + x = -6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -6.873863542 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.873863542 + -1.5 x = -6.873863542 + -1.5 Combine like terms: -6.873863542 + -1.5 = -8.373863542 x = -8.373863542 Simplifying x = -8.373863542Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.373863542, -8.373863542}
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