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Simplifying x2 + -13.5x + 38 = 0 Reorder the terms: 38 + -13.5x + x2 = 0 Solving 38 + -13.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-38' to each side of the equation. 38 + -13.5x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + -13.5x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -13.5x + x2 = 0 + -38 -13.5x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 -13.5x + x2 = -38 The x term is -13.5x. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5x + 45.5625 + x2 = -38 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = -38 + 45.5625 Combine like terms: -38 + 45.5625 = 7.5625 45.5625 + -13.5x + x2 = 7.5625 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 7.5625 Calculate the square root of the right side: 2.75 Break this problem into two subproblems by setting (x + -6.75) equal to 2.75 and -2.75.Subproblem 1
x + -6.75 = 2.75 Simplifying x + -6.75 = 2.75 Reorder the terms: -6.75 + x = 2.75 Solving -6.75 + x = 2.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = 2.75 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 2.75 + 6.75 x = 2.75 + 6.75 Combine like terms: 2.75 + 6.75 = 9.5 x = 9.5 Simplifying x = 9.5Subproblem 2
x + -6.75 = -2.75 Simplifying x + -6.75 = -2.75 Reorder the terms: -6.75 + x = -2.75 Solving -6.75 + x = -2.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = -2.75 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -2.75 + 6.75 x = -2.75 + 6.75 Combine like terms: -2.75 + 6.75 = 4 x = 4 Simplifying x = 4Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.5, 4}
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