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Simplifying x2 + 8x + 16 = 0.5625 Reorder the terms: 16 + 8x + x2 = 0.5625 Solving 16 + 8x + x2 = 0.5625 Solving for variable 'x'. Reorder the terms: 16 + -0.5625 + 8x + x2 = 0.5625 + -0.5625 Combine like terms: 16 + -0.5625 = 15.4375 15.4375 + 8x + x2 = 0.5625 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 15.4375 + 8x + x2 = 0.0000 Begin completing the square. Move the constant term to the right: Add '-15.4375' to each side of the equation. 15.4375 + 8x + -15.4375 + x2 = 0.0000 + -15.4375 Reorder the terms: 15.4375 + -15.4375 + 8x + x2 = 0.0000 + -15.4375 Combine like terms: 15.4375 + -15.4375 = 0.0000 0.0000 + 8x + x2 = 0.0000 + -15.4375 8x + x2 = 0.0000 + -15.4375 Combine like terms: 0.0000 + -15.4375 = -15.4375 8x + x2 = -15.4375 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -15.4375 + 16 Reorder the terms: 16 + 8x + x2 = -15.4375 + 16 Combine like terms: -15.4375 + 16 = 0.5625 16 + 8x + x2 = 0.5625 Factor a perfect square on the left side: (x + 4)(x + 4) = 0.5625 Calculate the square root of the right side: 0.75 Break this problem into two subproblems by setting (x + 4) equal to 0.75 and -0.75.Subproblem 1
x + 4 = 0.75 Simplifying x + 4 = 0.75 Reorder the terms: 4 + x = 0.75 Solving 4 + x = 0.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 0.75 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0.75 + -4 x = 0.75 + -4 Combine like terms: 0.75 + -4 = -3.25 x = -3.25 Simplifying x = -3.25Subproblem 2
x + 4 = -0.75 Simplifying x + 4 = -0.75 Reorder the terms: 4 + x = -0.75 Solving 4 + x = -0.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -0.75 + -4 Combine like terms: 4 + -4 = 0 0 + x = -0.75 + -4 x = -0.75 + -4 Combine like terms: -0.75 + -4 = -4.75 x = -4.75 Simplifying x = -4.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.25, -4.75}
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