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Simplifying x2 + 14x + 48 = 239.25 Reorder the terms: 48 + 14x + x2 = 239.25 Solving 48 + 14x + x2 = 239.25 Solving for variable 'x'. Reorder the terms: 48 + -239.25 + 14x + x2 = 239.25 + -239.25 Combine like terms: 48 + -239.25 = -191.25 -191.25 + 14x + x2 = 239.25 + -239.25 Combine like terms: 239.25 + -239.25 = 0.00 -191.25 + 14x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '191.25' to each side of the equation. -191.25 + 14x + 191.25 + x2 = 0.00 + 191.25 Reorder the terms: -191.25 + 191.25 + 14x + x2 = 0.00 + 191.25 Combine like terms: -191.25 + 191.25 = 0.00 0.00 + 14x + x2 = 0.00 + 191.25 14x + x2 = 0.00 + 191.25 Combine like terms: 0.00 + 191.25 = 191.25 14x + x2 = 191.25 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 = 191.25 + 49 Reorder the terms: 49 + 14x + x2 = 191.25 + 49 Combine like terms: 191.25 + 49 = 240.25 49 + 14x + x2 = 240.25 Factor a perfect square on the left side: (x + 7)(x + 7) = 240.25 Calculate the square root of the right side: 15.5 Break this problem into two subproblems by setting (x + 7) equal to 15.5 and -15.5.Subproblem 1
x + 7 = 15.5 Simplifying x + 7 = 15.5 Reorder the terms: 7 + x = 15.5 Solving 7 + x = 15.5 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 = 15.5 + -7 Combine like terms: 7 + -7 = 0 0 + x = 15.5 + -7 x = 15.5 + -7 Combine like terms: 15.5 + -7 = 8.5 x = 8.5 Simplifying x = 8.5Subproblem 2
x + 7 = -15.5 Simplifying x + 7 = -15.5 Reorder the terms: 7 + x = -15.5 Solving 7 + x = -15.5 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 = -15.5 + -7 Combine like terms: 7 + -7 = 0 0 + x = -15.5 + -7 x = -15.5 + -7 Combine like terms: -15.5 + -7 = -22.5 x = -22.5 Simplifying x = -22.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.5, -22.5}
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