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Simplifying x2 + 14x + 49 + -5 = 0.75 Reorder the terms: 49 + -5 + 14x + x2 = 0.75 Combine like terms: 49 + -5 = 44 44 + 14x + x2 = 0.75 Solving 44 + 14x + x2 = 0.75 Solving for variable 'x'. Reorder the terms: 44 + -0.75 + 14x + x2 = 0.75 + -0.75 Combine like terms: 44 + -0.75 = 43.25 43.25 + 14x + x2 = 0.75 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 43.25 + 14x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '-43.25' to each side of the equation. 43.25 + 14x + -43.25 + x2 = 0.00 + -43.25 Reorder the terms: 43.25 + -43.25 + 14x + x2 = 0.00 + -43.25 Combine like terms: 43.25 + -43.25 = 0.00 0.00 + 14x + x2 = 0.00 + -43.25 14x + x2 = 0.00 + -43.25 Combine like terms: 0.00 + -43.25 = -43.25 14x + x2 = -43.25 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 = -43.25 + 49 Reorder the terms: 49 + 14x + x2 = -43.25 + 49 Combine like terms: -43.25 + 49 = 5.75 49 + 14x + x2 = 5.75 Factor a perfect square on the left side: (x + 7)(x + 7) = 5.75 Calculate the square root of the right side: 2.397915762 Break this problem into two subproblems by setting (x + 7) equal to 2.397915762 and -2.397915762.Subproblem 1
x + 7 = 2.397915762 Simplifying x + 7 = 2.397915762 Reorder the terms: 7 + x = 2.397915762 Solving 7 + x = 2.397915762 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 = 2.397915762 + -7 Combine like terms: 7 + -7 = 0 0 + x = 2.397915762 + -7 x = 2.397915762 + -7 Combine like terms: 2.397915762 + -7 = -4.602084238 x = -4.602084238 Simplifying x = -4.602084238Subproblem 2
x + 7 = -2.397915762 Simplifying x + 7 = -2.397915762 Reorder the terms: 7 + x = -2.397915762 Solving 7 + x = -2.397915762 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 = -2.397915762 + -7 Combine like terms: 7 + -7 = 0 0 + x = -2.397915762 + -7 x = -2.397915762 + -7 Combine like terms: -2.397915762 + -7 = -9.397915762 x = -9.397915762 Simplifying x = -9.397915762Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.602084238, -9.397915762}
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