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Simplifying 2x2 + -20x + 8 = 31 + -4x + x2 Reorder the terms: 8 + -20x + 2x2 = 31 + -4x + x2 Solving 8 + -20x + 2x2 = 31 + -4x + x2 Solving for variable 'x'. Reorder the terms: 8 + -31 + -20x + 4x + 2x2 + -1x2 = 31 + -4x + x2 + -31 + 4x + -1x2 Combine like terms: 8 + -31 = -23 -23 + -20x + 4x + 2x2 + -1x2 = 31 + -4x + x2 + -31 + 4x + -1x2 Combine like terms: -20x + 4x = -16x -23 + -16x + 2x2 + -1x2 = 31 + -4x + x2 + -31 + 4x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -23 + -16x + 1x2 = 31 + -4x + x2 + -31 + 4x + -1x2 Reorder the terms: -23 + -16x + 1x2 = 31 + -31 + -4x + 4x + x2 + -1x2 Combine like terms: 31 + -31 = 0 -23 + -16x + 1x2 = 0 + -4x + 4x + x2 + -1x2 -23 + -16x + 1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 -23 + -16x + 1x2 = 0 + x2 + -1x2 -23 + -16x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -23 + -16x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -16x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + -16x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -16x + x2 = 0 + 23 -16x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 -16x + x2 = 23 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 23 + 64 Reorder the terms: 64 + -16x + x2 = 23 + 64 Combine like terms: 23 + 64 = 87 64 + -16x + x2 = 87 Factor a perfect square on the left side: (x + -8)(x + -8) = 87 Calculate the square root of the right side: 9.327379053 Break this problem into two subproblems by setting (x + -8) equal to 9.327379053 and -9.327379053.Subproblem 1
x + -8 = 9.327379053 Simplifying x + -8 = 9.327379053 Reorder the terms: -8 + x = 9.327379053 Solving -8 + x = 9.327379053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 9.327379053 + 8 Combine like terms: -8 + 8 = 0 0 + x = 9.327379053 + 8 x = 9.327379053 + 8 Combine like terms: 9.327379053 + 8 = 17.327379053 x = 17.327379053 Simplifying x = 17.327379053Subproblem 2
x + -8 = -9.327379053 Simplifying x + -8 = -9.327379053 Reorder the terms: -8 + x = -9.327379053 Solving -8 + x = -9.327379053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -9.327379053 + 8 Combine like terms: -8 + 8 = 0 0 + x = -9.327379053 + 8 x = -9.327379053 + 8 Combine like terms: -9.327379053 + 8 = -1.327379053 x = -1.327379053 Simplifying x = -1.327379053Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.327379053, -1.327379053}
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