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Simplifying 0.5x2 + 7x + 12 = 48 Reorder the terms: 12 + 7x + 0.5x2 = 48 Solving 12 + 7x + 0.5x2 = 48 Solving for variable 'x'. Reorder the terms: 12 + -48 + 7x + 0.5x2 = 48 + -48 Combine like terms: 12 + -48 = -36 -36 + 7x + 0.5x2 = 48 + -48 Combine like terms: 48 + -48 = 0 -36 + 7x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -72 + 14x + x2 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + 14x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + 14x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + 14x + x2 = 0 + 72 14x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 14x + x2 = 72 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 = 72 + 49 Reorder the terms: 49 + 14x + x2 = 72 + 49 Combine like terms: 72 + 49 = 121 49 + 14x + x2 = 121 Factor a perfect square on the left side: (x + 7)(x + 7) = 121 Calculate the square root of the right side: 11 Break this problem into two subproblems by setting (x + 7) equal to 11 and -11.Subproblem 1
x + 7 = 11 Simplifying x + 7 = 11 Reorder the terms: 7 + x = 11 Solving 7 + x = 11 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 = 11 + -7 Combine like terms: 7 + -7 = 0 0 + x = 11 + -7 x = 11 + -7 Combine like terms: 11 + -7 = 4 x = 4 Simplifying x = 4Subproblem 2
x + 7 = -11 Simplifying x + 7 = -11 Reorder the terms: 7 + x = -11 Solving 7 + x = -11 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 = -11 + -7 Combine like terms: 7 + -7 = 0 0 + x = -11 + -7 x = -11 + -7 Combine like terms: -11 + -7 = -18 x = -18 Simplifying x = -18Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -18}
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