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Simplifying x2 + 2.5x + -6 = 0 Reorder the terms: -6 + 2.5x + x2 = 0 Solving -6 + 2.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 2.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 2.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 2.5x + x2 = 0 + 6 2.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 2.5x + x2 = 6 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 6 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 6 + 1.5625 Combine like terms: 6 + 1.5625 = 7.5625 1.5625 + 2.5x + x2 = 7.5625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 7.5625 Calculate the square root of the right side: 2.75 Break this problem into two subproblems by setting (x + 1.25) equal to 2.75 and -2.75.Subproblem 1
x + 1.25 = 2.75 Simplifying x + 1.25 = 2.75 Reorder the terms: 1.25 + x = 2.75 Solving 1.25 + x = 2.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.75 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.75 + -1.25 x = 2.75 + -1.25 Combine like terms: 2.75 + -1.25 = 1.5 x = 1.5 Simplifying x = 1.5Subproblem 2
x + 1.25 = -2.75 Simplifying x + 1.25 = -2.75 Reorder the terms: 1.25 + x = -2.75 Solving 1.25 + x = -2.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.75 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.75 + -1.25 x = -2.75 + -1.25 Combine like terms: -2.75 + -1.25 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5, -4}
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