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Simplifying -0.1x2 + 0.9x + 2.2 = 0 Reorder the terms: 2.2 + 0.9x + -0.1x2 = 0 Solving 2.2 + 0.9x + -0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -22 + -9x + x2 = 0 Move the constant term to the right: Add '22' to each side of the equation. -22 + -9x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -9x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -9x + x2 = 0 + 22 -9x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -9x + x2 = 22 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 = 22 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 22 + 20.25 Combine like terms: 22 + 20.25 = 42.25 20.25 + -9x + x2 = 42.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 42.25 Calculate the square root of the right side: 6.5 Break this problem into two subproblems by setting (x + -4.5) equal to 6.5 and -6.5.Subproblem 1
x + -4.5 = 6.5 Simplifying x + -4.5 = 6.5 Reorder the terms: -4.5 + x = 6.5 Solving -4.5 + x = 6.5 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 = 6.5 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 6.5 + 4.5 x = 6.5 + 4.5 Combine like terms: 6.5 + 4.5 = 11 x = 11 Simplifying x = 11Subproblem 2
x + -4.5 = -6.5 Simplifying x + -4.5 = -6.5 Reorder the terms: -4.5 + x = -6.5 Solving -4.5 + x = -6.5 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 = -6.5 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -6.5 + 4.5 x = -6.5 + 4.5 Combine like terms: -6.5 + 4.5 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {11, -2}
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