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Simplifying -2x2 + 18x + 9 = 0 Reorder the terms: 9 + 18x + -2x2 = 0 Solving 9 + 18x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + -9x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -9x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -9x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -9x + x2 = 0 + 4.5 -9x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -9x + x2 = 4.5 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 = 4.5 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 4.5 + 20.25 Combine like terms: 4.5 + 20.25 = 24.75 20.25 + -9x + x2 = 24.75 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 24.75 Calculate the square root of the right side: 4.974937186 Break this problem into two subproblems by setting (x + -4.5) equal to 4.974937186 and -4.974937186.Subproblem 1
x + -4.5 = 4.974937186 Simplifying x + -4.5 = 4.974937186 Reorder the terms: -4.5 + x = 4.974937186 Solving -4.5 + x = 4.974937186 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 = 4.974937186 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 4.974937186 + 4.5 x = 4.974937186 + 4.5 Combine like terms: 4.974937186 + 4.5 = 9.474937186 x = 9.474937186 Simplifying x = 9.474937186Subproblem 2
x + -4.5 = -4.974937186 Simplifying x + -4.5 = -4.974937186 Reorder the terms: -4.5 + x = -4.974937186 Solving -4.5 + x = -4.974937186 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 = -4.974937186 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -4.974937186 + 4.5 x = -4.974937186 + 4.5 Combine like terms: -4.974937186 + 4.5 = -0.474937186 x = -0.474937186 Simplifying x = -0.474937186Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.474937186, -0.474937186}
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