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Simplifying x2 + 7.5x + 9 = 0 Reorder the terms: 9 + 7.5x + x2 = 0 Solving 9 + 7.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 7.5x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 7.5x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 7.5x + x2 = 0 + -9 7.5x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 7.5x + x2 = -9 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = -9 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = -9 + 14.0625 Combine like terms: -9 + 14.0625 = 5.0625 14.0625 + 7.5x + x2 = 5.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 5.0625 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (x + 3.75) equal to 2.25 and -2.25.Subproblem 1
x + 3.75 = 2.25 Simplifying x + 3.75 = 2.25 Reorder the terms: 3.75 + x = 2.25 Solving 3.75 + x = 2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 2.25 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 2.25 + -3.75 x = 2.25 + -3.75 Combine like terms: 2.25 + -3.75 = -1.5 x = -1.5 Simplifying x = -1.5Subproblem 2
x + 3.75 = -2.25 Simplifying x + 3.75 = -2.25 Reorder the terms: 3.75 + x = -2.25 Solving 3.75 + x = -2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -2.25 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -2.25 + -3.75 x = -2.25 + -3.75 Combine like terms: -2.25 + -3.75 = -6 x = -6 Simplifying x = -6Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.5, -6}
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