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Simplifying 9x2 + -11x + 4 = 8x2 + 20 Reorder the terms: 4 + -11x + 9x2 = 8x2 + 20 Reorder the terms: 4 + -11x + 9x2 = 20 + 8x2 Solving 4 + -11x + 9x2 = 20 + 8x2 Solving for variable 'x'. Reorder the terms: 4 + -20 + -11x + 9x2 + -8x2 = 20 + 8x2 + -20 + -8x2 Combine like terms: 4 + -20 = -16 -16 + -11x + 9x2 + -8x2 = 20 + 8x2 + -20 + -8x2 Combine like terms: 9x2 + -8x2 = 1x2 -16 + -11x + 1x2 = 20 + 8x2 + -20 + -8x2 Reorder the terms: -16 + -11x + 1x2 = 20 + -20 + 8x2 + -8x2 Combine like terms: 20 + -20 = 0 -16 + -11x + 1x2 = 0 + 8x2 + -8x2 -16 + -11x + 1x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 -16 + -11x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -11x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -11x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -11x + x2 = 0 + 16 -11x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -11x + x2 = 16 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 16 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 16 + 30.25 Combine like terms: 16 + 30.25 = 46.25 30.25 + -11x + x2 = 46.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (x + -5.5) equal to 6.800735254 and -6.800735254.Subproblem 1
x + -5.5 = 6.800735254 Simplifying x + -5.5 = 6.800735254 Reorder the terms: -5.5 + x = 6.800735254 Solving -5.5 + x = 6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 6.800735254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.800735254 + 5.5 x = 6.800735254 + 5.5 Combine like terms: 6.800735254 + 5.5 = 12.300735254 x = 12.300735254 Simplifying x = 12.300735254Subproblem 2
x + -5.5 = -6.800735254 Simplifying x + -5.5 = -6.800735254 Reorder the terms: -5.5 + x = -6.800735254 Solving -5.5 + x = -6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -6.800735254 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.800735254 + 5.5 x = -6.800735254 + 5.5 Combine like terms: -6.800735254 + 5.5 = -1.300735254 x = -1.300735254 Simplifying x = -1.300735254Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.300735254, -1.300735254}
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