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Simplifying 0.25x2 + 3.5x = -12 Reorder the terms: 3.5x + 0.25x2 = -12 Solving 3.5x + 0.25x2 = -12 Solving for variable 'x'. Reorder the terms: 12 + 3.5x + 0.25x2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + 3.5x + 0.25x2 = 0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. 48 + 14x + x2 = 0 Move the constant term to the right: Add '-48' to each side of the equation. 48 + 14x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + 14x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + 14x + x2 = 0 + -48 14x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 14x + x2 = -48 The x term is 14x. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x + 49 + x2 = -48 + 49 Reorder the terms: 49 + 14x + x2 = -48 + 49 Combine like terms: -48 + 49 = 1 49 + 14x + x2 = 1 Factor a perfect square on the left side: (x + 7)(x + 7) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + 7) equal to 1 and -1.Subproblem 1
x + 7 = 1 Simplifying x + 7 = 1 Reorder the terms: 7 + x = 1 Solving 7 + x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 1 + -7 Combine like terms: 7 + -7 = 0 0 + x = 1 + -7 x = 1 + -7 Combine like terms: 1 + -7 = -6 x = -6 Simplifying x = -6Subproblem 2
x + 7 = -1 Simplifying x + 7 = -1 Reorder the terms: 7 + x = -1 Solving 7 + x = -1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -1 + -7 Combine like terms: 7 + -7 = 0 0 + x = -1 + -7 x = -1 + -7 Combine like terms: -1 + -7 = -8 x = -8 Simplifying x = -8Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6, -8}
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