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Simplifying 0.1x2 + -0.3x + -27 = 0 Reorder the terms: -27 + -0.3x + 0.1x2 = 0 Solving -27 + -0.3x + 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'. -270 + -3x + x2 = 0 Move the constant term to the right: Add '270' to each side of the equation. -270 + -3x + 270 + x2 = 0 + 270 Reorder the terms: -270 + 270 + -3x + x2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + -3x + x2 = 0 + 270 -3x + x2 = 0 + 270 Combine like terms: 0 + 270 = 270 -3x + x2 = 270 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 270 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 270 + 2.25 Combine like terms: 270 + 2.25 = 272.25 2.25 + -3x + x2 = 272.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 272.25 Calculate the square root of the right side: 16.5 Break this problem into two subproblems by setting (x + -1.5) equal to 16.5 and -16.5.Subproblem 1
x + -1.5 = 16.5 Simplifying x + -1.5 = 16.5 Reorder the terms: -1.5 + x = 16.5 Solving -1.5 + x = 16.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 16.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 16.5 + 1.5 x = 16.5 + 1.5 Combine like terms: 16.5 + 1.5 = 18 x = 18 Simplifying x = 18Subproblem 2
x + -1.5 = -16.5 Simplifying x + -1.5 = -16.5 Reorder the terms: -1.5 + x = -16.5 Solving -1.5 + x = -16.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -16.5 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -16.5 + 1.5 x = -16.5 + 1.5 Combine like terms: -16.5 + 1.5 = -15 x = -15 Simplifying x = -15Solution
The solution to the problem is based on the solutions from the subproblems. x = {18, -15}
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