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Simplifying x2 + -9x + 20.25 = 0 Reorder the terms: 20.25 + -9x + x2 = 0 Solving 20.25 + -9x + x2 = 0 Solving for variable 'x'. Begin completing the square. 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 = 0.00 20.25 + -9x + x2 = 0.00 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (x + -4.5) equal to 0.00 and 0.00.Subproblem 1
x + -4.5 = 0.00 Simplifying x + -4.5 = 0.00 Reorder the terms: -4.5 + x = 0.00 Solving -4.5 + x = 0.00 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 = 0.00 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 0.00 + 4.5 x = 0.00 + 4.5 Combine like terms: 0.00 + 4.5 = 4.5 x = 4.5 Simplifying x = 4.5Subproblem 2
x + -4.5 = 0.00 Simplifying x + -4.5 = 0.00 Reorder the terms: -4.5 + x = 0.00 Solving -4.5 + x = 0.00 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 = 0.00 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 0.00 + 4.5 x = 0.00 + 4.5 Combine like terms: 0.00 + 4.5 = 4.5 x = 4.5 Simplifying x = 4.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.5, 4.5}
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