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Simplifying x2 + -9x + 6 = 49 Reorder the terms: 6 + -9x + x2 = 49 Solving 6 + -9x + x2 = 49 Solving for variable 'x'. Reorder the terms: 6 + -49 + -9x + x2 = 49 + -49 Combine like terms: 6 + -49 = -43 -43 + -9x + x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -43 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '43' to each side of the equation. -43 + -9x + 43 + x2 = 0 + 43 Reorder the terms: -43 + 43 + -9x + x2 = 0 + 43 Combine like terms: -43 + 43 = 0 0 + -9x + x2 = 0 + 43 -9x + x2 = 0 + 43 Combine like terms: 0 + 43 = 43 -9x + x2 = 43 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 43 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 43 + 20.25 Combine like terms: 43 + 20.25 = 63.25 20.25 + -9x + x2 = 63.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 63.25 Calculate the square root of the right side: 7.95298686 Break this problem into two subproblems by setting (x + -4.5) equal to 7.95298686 and -7.95298686.Subproblem 1
x + -4.5 = 7.95298686 Simplifying x + -4.5 = 7.95298686 Reorder the terms: -4.5 + x = 7.95298686 Solving -4.5 + x = 7.95298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 7.95298686 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 7.95298686 + 4.5 x = 7.95298686 + 4.5 Combine like terms: 7.95298686 + 4.5 = 12.45298686 x = 12.45298686 Simplifying x = 12.45298686Subproblem 2
x + -4.5 = -7.95298686 Simplifying x + -4.5 = -7.95298686 Reorder the terms: -4.5 + x = -7.95298686 Solving -4.5 + x = -7.95298686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -7.95298686 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -7.95298686 + 4.5 x = -7.95298686 + 4.5 Combine like terms: -7.95298686 + 4.5 = -3.45298686 x = -3.45298686 Simplifying x = -3.45298686Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.45298686, -3.45298686}
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