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Simplifying -0.1x2 + 0.5x + 0.6 = 0 Reorder the terms: 0.6 + 0.5x + -0.1x2 = 0 Solving 0.6 + 0.5x + -0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -6 + -5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5x + x2 = 0 + 6 -5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -5x + x2 = 6 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 6 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 6 + 6.25 Combine like terms: 6 + 6.25 = 12.25 6.25 + -5x + x2 = 12.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 12.25 Calculate the square root of the right side: 3.5 Break this problem into two subproblems by setting (x + -2.5) equal to 3.5 and -3.5.Subproblem 1
x + -2.5 = 3.5 Simplifying x + -2.5 = 3.5 Reorder the terms: -2.5 + x = 3.5 Solving -2.5 + x = 3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.5 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.5 + 2.5 x = 3.5 + 2.5 Combine like terms: 3.5 + 2.5 = 6 x = 6 Simplifying x = 6Subproblem 2
x + -2.5 = -3.5 Simplifying x + -2.5 = -3.5 Reorder the terms: -2.5 + x = -3.5 Solving -2.5 + x = -3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.5 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.5 + 2.5 x = -3.5 + 2.5 Combine like terms: -3.5 + 2.5 = -1 x = -1 Simplifying x = -1Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, -1}
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