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Simplifying 0.0216 + -0.3x + x2 = 0 Solving 0.0216 + -0.3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.0216' to each side of the equation. 0.0216 + -0.3x + -0.0216 + x2 = 0 + -0.0216 Reorder the terms: 0.0216 + -0.0216 + -0.3x + x2 = 0 + -0.0216 Combine like terms: 0.0216 + -0.0216 = 0.0000 0.0000 + -0.3x + x2 = 0 + -0.0216 -0.3x + x2 = 0 + -0.0216 Combine like terms: 0 + -0.0216 = -0.0216 -0.3x + x2 = -0.0216 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 = -0.0216 + 0.0225 Reorder the terms: 0.0225 + -0.3x + x2 = -0.0216 + 0.0225 Combine like terms: -0.0216 + 0.0225 = 0.0009 0.0225 + -0.3x + x2 = 0.0009 Factor a perfect square on the left side: (x + -0.15)(x + -0.15) = 0.0009 Calculate the square root of the right side: 0.03 Break this problem into two subproblems by setting (x + -0.15) equal to 0.03 and -0.03.Subproblem 1
x + -0.15 = 0.03 Simplifying x + -0.15 = 0.03 Reorder the terms: -0.15 + x = 0.03 Solving -0.15 + x = 0.03 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 = 0.03 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = 0.03 + 0.15 x = 0.03 + 0.15 Combine like terms: 0.03 + 0.15 = 0.18 x = 0.18 Simplifying x = 0.18Subproblem 2
x + -0.15 = -0.03 Simplifying x + -0.15 = -0.03 Reorder the terms: -0.15 + x = -0.03 Solving -0.15 + x = -0.03 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 = -0.03 + 0.15 Combine like terms: -0.15 + 0.15 = 0.00 0.00 + x = -0.03 + 0.15 x = -0.03 + 0.15 Combine like terms: -0.03 + 0.15 = 0.12 x = 0.12 Simplifying x = 0.12Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.18, 0.12}
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