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Simplifying x2 + 0.3x + -5.5 = 0 Reorder the terms: -5.5 + 0.3x + x2 = 0 Solving -5.5 + 0.3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 0.3x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 0.3x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 0.3x + x2 = 0 + 5.5 0.3x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 0.3x + x2 = 5.5 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 5.5 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 5.5 + 0.0225 Combine like terms: 5.5 + 0.0225 = 5.5225 0.0225 + 0.3x + x2 = 5.5225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 5.5225 Calculate the square root of the right side: 2.35 Break this problem into two subproblems by setting (x + 0.15) equal to 2.35 and -2.35.Subproblem 1
x + 0.15 = 2.35 Simplifying x + 0.15 = 2.35 Reorder the terms: 0.15 + x = 2.35 Solving 0.15 + x = 2.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 2.35 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 2.35 + -0.15 x = 2.35 + -0.15 Combine like terms: 2.35 + -0.15 = 2.2 x = 2.2 Simplifying x = 2.2Subproblem 2
x + 0.15 = -2.35 Simplifying x + 0.15 = -2.35 Reorder the terms: 0.15 + x = -2.35 Solving 0.15 + x = -2.35 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -2.35 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -2.35 + -0.15 x = -2.35 + -0.15 Combine like terms: -2.35 + -0.15 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2, -2.5}
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