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Simplifying -0.9x2 + -2.7x + 25.2 = 0 Reorder the terms: 25.2 + -2.7x + -0.9x2 = 0 Solving 25.2 + -2.7x + -0.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.9 the coefficient of the squared term: Divide each side by '-0.9'. -28 + 3x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 3x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 3x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 3x + x2 = 0 + 28 3x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 3x + x2 = 28 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 = 28 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 28 + 2.25 Combine like terms: 28 + 2.25 = 30.25 2.25 + 3x + x2 = 30.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 30.25 Calculate the square root of the right side: 5.5 Break this problem into two subproblems by setting (x + 1.5) equal to 5.5 and -5.5.Subproblem 1
x + 1.5 = 5.5 Simplifying x + 1.5 = 5.5 Reorder the terms: 1.5 + x = 5.5 Solving 1.5 + x = 5.5 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 = 5.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5.5 + -1.5 x = 5.5 + -1.5 Combine like terms: 5.5 + -1.5 = 4 x = 4 Simplifying x = 4Subproblem 2
x + 1.5 = -5.5 Simplifying x + 1.5 = -5.5 Reorder the terms: 1.5 + x = -5.5 Solving 1.5 + x = -5.5 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 = -5.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5.5 + -1.5 x = -5.5 + -1.5 Combine like terms: -5.5 + -1.5 = -7 x = -7 Simplifying x = -7Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -7}
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