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Simplifying 4x2 + 31x + -45 = 3x2 + 52x + -17 Reorder the terms: -45 + 31x + 4x2 = 3x2 + 52x + -17 Reorder the terms: -45 + 31x + 4x2 = -17 + 52x + 3x2 Solving -45 + 31x + 4x2 = -17 + 52x + 3x2 Solving for variable 'x'. Reorder the terms: -45 + 17 + 31x + -52x + 4x2 + -3x2 = -17 + 52x + 3x2 + 17 + -52x + -3x2 Combine like terms: -45 + 17 = -28 -28 + 31x + -52x + 4x2 + -3x2 = -17 + 52x + 3x2 + 17 + -52x + -3x2 Combine like terms: 31x + -52x = -21x -28 + -21x + 4x2 + -3x2 = -17 + 52x + 3x2 + 17 + -52x + -3x2 Combine like terms: 4x2 + -3x2 = 1x2 -28 + -21x + 1x2 = -17 + 52x + 3x2 + 17 + -52x + -3x2 Reorder the terms: -28 + -21x + 1x2 = -17 + 17 + 52x + -52x + 3x2 + -3x2 Combine like terms: -17 + 17 = 0 -28 + -21x + 1x2 = 0 + 52x + -52x + 3x2 + -3x2 -28 + -21x + 1x2 = 52x + -52x + 3x2 + -3x2 Combine like terms: 52x + -52x = 0 -28 + -21x + 1x2 = 0 + 3x2 + -3x2 -28 + -21x + 1x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -28 + -21x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '28' to each side of the equation. -28 + -21x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + -21x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + -21x + x2 = 0 + 28 -21x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 -21x + x2 = 28 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = 28 + 110.25 Reorder the terms: 110.25 + -21x + x2 = 28 + 110.25 Combine like terms: 28 + 110.25 = 138.25 110.25 + -21x + x2 = 138.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 138.25 Calculate the square root of the right side: 11.757976016 Break this problem into two subproblems by setting (x + -10.5) equal to 11.757976016 and -11.757976016.Subproblem 1
x + -10.5 = 11.757976016 Simplifying x + -10.5 = 11.757976016 Reorder the terms: -10.5 + x = 11.757976016 Solving -10.5 + x = 11.757976016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 11.757976016 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 11.757976016 + 10.5 x = 11.757976016 + 10.5 Combine like terms: 11.757976016 + 10.5 = 22.257976016 x = 22.257976016 Simplifying x = 22.257976016Subproblem 2
x + -10.5 = -11.757976016 Simplifying x + -10.5 = -11.757976016 Reorder the terms: -10.5 + x = -11.757976016 Solving -10.5 + x = -11.757976016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -11.757976016 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -11.757976016 + 10.5 x = -11.757976016 + 10.5 Combine like terms: -11.757976016 + 10.5 = -1.257976016 x = -1.257976016 Simplifying x = -1.257976016Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.257976016, -1.257976016}
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