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Simplifying x2 + -10.5x + 27 = 0 Reorder the terms: 27 + -10.5x + x2 = 0 Solving 27 + -10.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-27' to each side of the equation. 27 + -10.5x + -27 + x2 = 0 + -27 Reorder the terms: 27 + -27 + -10.5x + x2 = 0 + -27 Combine like terms: 27 + -27 = 0 0 + -10.5x + x2 = 0 + -27 -10.5x + x2 = 0 + -27 Combine like terms: 0 + -27 = -27 -10.5x + x2 = -27 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = -27 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -27 + 27.5625 Combine like terms: -27 + 27.5625 = 0.5625 27.5625 + -10.5x + x2 = 0.5625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 0.5625 Calculate the square root of the right side: 0.75 Break this problem into two subproblems by setting (x + -5.25) equal to 0.75 and -0.75.Subproblem 1
x + -5.25 = 0.75 Simplifying x + -5.25 = 0.75 Reorder the terms: -5.25 + x = 0.75 Solving -5.25 + x = 0.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 0.75 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 0.75 + 5.25 x = 0.75 + 5.25 Combine like terms: 0.75 + 5.25 = 6 x = 6 Simplifying x = 6Subproblem 2
x + -5.25 = -0.75 Simplifying x + -5.25 = -0.75 Reorder the terms: -5.25 + x = -0.75 Solving -5.25 + x = -0.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -0.75 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -0.75 + 5.25 x = -0.75 + 5.25 Combine like terms: -0.75 + 5.25 = 4.5 x = 4.5 Simplifying x = 4.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, 4.5}
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