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Simplifying x2 + -7x + 3 = 20 Reorder the terms: 3 + -7x + x2 = 20 Solving 3 + -7x + x2 = 20 Solving for variable 'x'. Reorder the terms: 3 + -20 + -7x + x2 = 20 + -20 Combine like terms: 3 + -20 = -17 -17 + -7x + x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -17 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -7x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -7x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -7x + x2 = 0 + 17 -7x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -7x + x2 = 17 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 17 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 17 + 12.25 Combine like terms: 17 + 12.25 = 29.25 12.25 + -7x + x2 = 29.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x + -3.5) equal to 5.408326913 and -5.408326913.Subproblem 1
x + -3.5 = 5.408326913 Simplifying x + -3.5 = 5.408326913 Reorder the terms: -3.5 + x = 5.408326913 Solving -3.5 + x = 5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 5.408326913 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 5.408326913 + 3.5 x = 5.408326913 + 3.5 Combine like terms: 5.408326913 + 3.5 = 8.908326913 x = 8.908326913 Simplifying x = 8.908326913Subproblem 2
x + -3.5 = -5.408326913 Simplifying x + -3.5 = -5.408326913 Reorder the terms: -3.5 + x = -5.408326913 Solving -3.5 + x = -5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -5.408326913 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -5.408326913 + 3.5 x = -5.408326913 + 3.5 Combine like terms: -5.408326913 + 3.5 = -1.908326913 x = -1.908326913 Simplifying x = -1.908326913Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.908326913, -1.908326913}
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