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Simplifying 0.25x2 + 1.5x + -6.75 = 0 Reorder the terms: -6.75 + 1.5x + 0.25x2 = 0 Solving -6.75 + 1.5x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -27 + 6x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + 6x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 6x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 6x + x2 = 0 + 27 6x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 6x + x2 = 27 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 27 + 9 Reorder the terms: 9 + 6x + x2 = 27 + 9 Combine like terms: 27 + 9 = 36 9 + 6x + x2 = 36 Factor a perfect square on the left side: (x + 3)(x + 3) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (x + 3) equal to 6 and -6.Subproblem 1
x + 3 = 6 Simplifying x + 3 = 6 Reorder the terms: 3 + x = 6 Solving 3 + x = 6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 6 + -3 Combine like terms: 3 + -3 = 0 0 + x = 6 + -3 x = 6 + -3 Combine like terms: 6 + -3 = 3 x = 3 Simplifying x = 3Subproblem 2
x + 3 = -6 Simplifying x + 3 = -6 Reorder the terms: 3 + x = -6 Solving 3 + x = -6 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -6 + -3 Combine like terms: 3 + -3 = 0 0 + x = -6 + -3 x = -6 + -3 Combine like terms: -6 + -3 = -9 x = -9 Simplifying x = -9Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -9}
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