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Simplifying x2 + 2.5x = 0.8 Reorder the terms: 2.5x + x2 = 0.8 Solving 2.5x + x2 = 0.8 Solving for variable 'x'. Reorder the terms: -0.8 + 2.5x + x2 = 0.8 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 -0.8 + 2.5x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 2.5x + 0.8 + x2 = 0.0 + 0.8 Reorder the terms: -0.8 + 0.8 + 2.5x + x2 = 0.0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 2.5x + x2 = 0.0 + 0.8 2.5x + x2 = 0.0 + 0.8 Combine like terms: 0.0 + 0.8 = 0.8 2.5x + x2 = 0.8 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 = 0.8 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 0.8 + 1.5625 Combine like terms: 0.8 + 1.5625 = 2.3625 1.5625 + 2.5x + x2 = 2.3625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 2.3625 Calculate the square root of the right side: 1.537042615 Break this problem into two subproblems by setting (x + 1.25) equal to 1.537042615 and -1.537042615.Subproblem 1
x + 1.25 = 1.537042615 Simplifying x + 1.25 = 1.537042615 Reorder the terms: 1.25 + x = 1.537042615 Solving 1.25 + x = 1.537042615 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 = 1.537042615 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.537042615 + -1.25 x = 1.537042615 + -1.25 Combine like terms: 1.537042615 + -1.25 = 0.287042615 x = 0.287042615 Simplifying x = 0.287042615Subproblem 2
x + 1.25 = -1.537042615 Simplifying x + 1.25 = -1.537042615 Reorder the terms: 1.25 + x = -1.537042615 Solving 1.25 + x = -1.537042615 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 = -1.537042615 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.537042615 + -1.25 x = -1.537042615 + -1.25 Combine like terms: -1.537042615 + -1.25 = -2.787042615 x = -2.787042615 Simplifying x = -2.787042615Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.287042615, -2.787042615}
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