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Simplifying x2 + 2.75x + 1.9 = 6.9 Reorder the terms: 1.9 + 2.75x + x2 = 6.9 Solving 1.9 + 2.75x + x2 = 6.9 Solving for variable 'x'. Reorder the terms: 1.9 + -6.9 + 2.75x + x2 = 6.9 + -6.9 Combine like terms: 1.9 + -6.9 = -5 -5 + 2.75x + x2 = 6.9 + -6.9 Combine like terms: 6.9 + -6.9 = 0.0 -5 + 2.75x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2.75x + 5 + x2 = 0.0 + 5 Reorder the terms: -5 + 5 + 2.75x + x2 = 0.0 + 5 Combine like terms: -5 + 5 = 0 0 + 2.75x + x2 = 0.0 + 5 2.75x + x2 = 0.0 + 5 Combine like terms: 0.0 + 5 = 5 2.75x + x2 = 5 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = 5 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 5 + 1.890625 Combine like terms: 5 + 1.890625 = 6.890625 1.890625 + 2.75x + x2 = 6.890625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 6.890625 Calculate the square root of the right side: 2.625 Break this problem into two subproblems by setting (x + 1.375) equal to 2.625 and -2.625.Subproblem 1
x + 1.375 = 2.625 Simplifying x + 1.375 = 2.625 Reorder the terms: 1.375 + x = 2.625 Solving 1.375 + x = 2.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 2.625 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 2.625 + -1.375 x = 2.625 + -1.375 Combine like terms: 2.625 + -1.375 = 1.25 x = 1.25 Simplifying x = 1.25Subproblem 2
x + 1.375 = -2.625 Simplifying x + 1.375 = -2.625 Reorder the terms: 1.375 + x = -2.625 Solving 1.375 + x = -2.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -2.625 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -2.625 + -1.375 x = -2.625 + -1.375 Combine like terms: -2.625 + -1.375 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.25, -4}
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