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Simplifying 0.2x2 + -1.4x + 0.1 = 0 Reorder the terms: 0.1 + -1.4x + 0.2x2 = 0 Solving 0.1 + -1.4x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 0.5 + -7x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -7x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -7x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -7x + x2 = 0 + -0.5 -7x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -7x + x2 = -0.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -0.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -0.5 + 12.25 Combine like terms: -0.5 + 12.25 = 11.75 12.25 + -7x + x2 = 11.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 11.75 Calculate the square root of the right side: 3.4278273 Break this problem into two subproblems by setting (x + -3.5) equal to 3.4278273 and -3.4278273.Subproblem 1
x + -3.5 = 3.4278273 Simplifying x + -3.5 = 3.4278273 Reorder the terms: -3.5 + x = 3.4278273 Solving -3.5 + x = 3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.4278273 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.4278273 + 3.5 x = 3.4278273 + 3.5 Combine like terms: 3.4278273 + 3.5 = 6.9278273 x = 6.9278273 Simplifying x = 6.9278273Subproblem 2
x + -3.5 = -3.4278273 Simplifying x + -3.5 = -3.4278273 Reorder the terms: -3.5 + x = -3.4278273 Solving -3.5 + x = -3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.4278273 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.4278273 + 3.5 x = -3.4278273 + 3.5 Combine like terms: -3.4278273 + 3.5 = 0.0721727 x = 0.0721727 Simplifying x = 0.0721727Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.9278273, 0.0721727}
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