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Simplifying 36x + -4x2 + 81 = 0 Reorder the terms: 81 + 36x + -4x2 = 0 Solving 81 + 36x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -20.25 + -9x + x2 = 0 Move the constant term to the right: Add '20.25' to each side of the equation. -20.25 + -9x + 20.25 + x2 = 0 + 20.25 Reorder the terms: -20.25 + 20.25 + -9x + x2 = 0 + 20.25 Combine like terms: -20.25 + 20.25 = 0.00 0.00 + -9x + x2 = 0 + 20.25 -9x + x2 = 0 + 20.25 Combine like terms: 0 + 20.25 = 20.25 -9x + x2 = 20.25 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 = 20.25 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 20.25 + 20.25 Combine like terms: 20.25 + 20.25 = 40.5 20.25 + -9x + x2 = 40.5 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 40.5 Calculate the square root of the right side: 6.363961031 Break this problem into two subproblems by setting (x + -4.5) equal to 6.363961031 and -6.363961031.Subproblem 1
x + -4.5 = 6.363961031 Simplifying x + -4.5 = 6.363961031 Reorder the terms: -4.5 + x = 6.363961031 Solving -4.5 + x = 6.363961031 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 = 6.363961031 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6.363961031 + 4.5 x = 6.363961031 + 4.5 Combine like terms: 6.363961031 + 4.5 = 10.863961031 x = 10.863961031 Simplifying x = 10.863961031Subproblem 2
x + -4.5 = -6.363961031 Simplifying x + -4.5 = -6.363961031 Reorder the terms: -4.5 + x = -6.363961031 Solving -4.5 + x = -6.363961031 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 = -6.363961031 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6.363961031 + 4.5 x = -6.363961031 + 4.5 Combine like terms: -6.363961031 + 4.5 = -1.863961031 x = -1.863961031 Simplifying x = -1.863961031Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.863961031, -1.863961031}
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