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Simplifying x2 + 14x + 49 = 3.0625 Reorder the terms: 49 + 14x + x2 = 3.0625 Solving 49 + 14x + x2 = 3.0625 Solving for variable 'x'. Reorder the terms: 49 + -3.0625 + 14x + x2 = 3.0625 + -3.0625 Combine like terms: 49 + -3.0625 = 45.9375 45.9375 + 14x + x2 = 3.0625 + -3.0625 Combine like terms: 3.0625 + -3.0625 = 0.0000 45.9375 + 14x + x2 = 0.0000 Begin completing the square. Move the constant term to the right: Add '-45.9375' to each side of the equation. 45.9375 + 14x + -45.9375 + x2 = 0.0000 + -45.9375 Reorder the terms: 45.9375 + -45.9375 + 14x + x2 = 0.0000 + -45.9375 Combine like terms: 45.9375 + -45.9375 = 0.0000 0.0000 + 14x + x2 = 0.0000 + -45.9375 14x + x2 = 0.0000 + -45.9375 Combine like terms: 0.0000 + -45.9375 = -45.9375 14x + x2 = -45.9375 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 = -45.9375 + 49 Reorder the terms: 49 + 14x + x2 = -45.9375 + 49 Combine like terms: -45.9375 + 49 = 3.0625 49 + 14x + x2 = 3.0625 Factor a perfect square on the left side: (x + 7)(x + 7) = 3.0625 Calculate the square root of the right side: 1.75 Break this problem into two subproblems by setting (x + 7) equal to 1.75 and -1.75.Subproblem 1
x + 7 = 1.75 Simplifying x + 7 = 1.75 Reorder the terms: 7 + x = 1.75 Solving 7 + x = 1.75 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 = 1.75 + -7 Combine like terms: 7 + -7 = 0 0 + x = 1.75 + -7 x = 1.75 + -7 Combine like terms: 1.75 + -7 = -5.25 x = -5.25 Simplifying x = -5.25Subproblem 2
x + 7 = -1.75 Simplifying x + 7 = -1.75 Reorder the terms: 7 + x = -1.75 Solving 7 + x = -1.75 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 = -1.75 + -7 Combine like terms: 7 + -7 = 0 0 + x = -1.75 + -7 x = -1.75 + -7 Combine like terms: -1.75 + -7 = -8.75 x = -8.75 Simplifying x = -8.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.25, -8.75}
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