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Simplifying x2 + 2.5x + 1.56 = 2 Reorder the terms: 1.56 + 2.5x + x2 = 2 Solving 1.56 + 2.5x + x2 = 2 Solving for variable 'x'. Reorder the terms: 1.56 + -2 + 2.5x + x2 = 2 + -2 Combine like terms: 1.56 + -2 = -0.44 -0.44 + 2.5x + x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -0.44 + 2.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '0.44' to each side of the equation. -0.44 + 2.5x + 0.44 + x2 = 0 + 0.44 Reorder the terms: -0.44 + 0.44 + 2.5x + x2 = 0 + 0.44 Combine like terms: -0.44 + 0.44 = 0.00 0.00 + 2.5x + x2 = 0 + 0.44 2.5x + x2 = 0 + 0.44 Combine like terms: 0 + 0.44 = 0.44 2.5x + x2 = 0.44 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 = 0.44 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 0.44 + 1.5625 Combine like terms: 0.44 + 1.5625 = 2.0025 1.5625 + 2.5x + x2 = 2.0025 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 2.0025 Calculate the square root of the right side: 1.41509717 Break this problem into two subproblems by setting (x + 1.25) equal to 1.41509717 and -1.41509717.Subproblem 1
x + 1.25 = 1.41509717 Simplifying x + 1.25 = 1.41509717 Reorder the terms: 1.25 + x = 1.41509717 Solving 1.25 + x = 1.41509717 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 = 1.41509717 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.41509717 + -1.25 x = 1.41509717 + -1.25 Combine like terms: 1.41509717 + -1.25 = 0.16509717 x = 0.16509717 Simplifying x = 0.16509717Subproblem 2
x + 1.25 = -1.41509717 Simplifying x + 1.25 = -1.41509717 Reorder the terms: 1.25 + x = -1.41509717 Solving 1.25 + x = -1.41509717 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 = -1.41509717 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.41509717 + -1.25 x = -1.41509717 + -1.25 Combine like terms: -1.41509717 + -1.25 = -2.66509717 x = -2.66509717 Simplifying x = -2.66509717Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.16509717, -2.66509717}
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