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Simplifying 27 = (x2 + -0.4x) Reorder the terms: 27 = (-0.4x + x2) Remove parenthesis around (-0.4x + x2) 27 = -0.4x + x2 Solving 27 = -0.4x + x2 Solving for variable 'x'. Reorder the terms: 27 + 0.4x + -1x2 = -0.4x + 0.4x + x2 + -1x2 Combine like terms: -0.4x + 0.4x = 0.0 27 + 0.4x + -1x2 = 0.0 + x2 + -1x2 27 + 0.4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 27 + 0.4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -27 + -0.4x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + -0.4x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + -0.4x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -0.4x + x2 = 0 + 27 -0.4x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 -0.4x + x2 = 27 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 27 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 27 + 0.04 Combine like terms: 27 + 0.04 = 27.04 0.04 + -0.4x + x2 = 27.04 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 27.04 Calculate the square root of the right side: 5.2 Break this problem into two subproblems by setting (x + -0.2) equal to 5.2 and -5.2.Subproblem 1
x + -0.2 = 5.2 Simplifying x + -0.2 = 5.2 Reorder the terms: -0.2 + x = 5.2 Solving -0.2 + x = 5.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 5.2 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 5.2 + 0.2 x = 5.2 + 0.2 Combine like terms: 5.2 + 0.2 = 5.4 x = 5.4 Simplifying x = 5.4Subproblem 2
x + -0.2 = -5.2 Simplifying x + -0.2 = -5.2 Reorder the terms: -0.2 + x = -5.2 Solving -0.2 + x = -5.2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -5.2 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -5.2 + 0.2 x = -5.2 + 0.2 Combine like terms: -5.2 + 0.2 = -5 x = -5 Simplifying x = -5Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.4, -5}
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