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Simplifying x2 + 8x + 15.75 = 0 Reorder the terms: 15.75 + 8x + x2 = 0 Solving 15.75 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15.75' to each side of the equation. 15.75 + 8x + -15.75 + x2 = 0 + -15.75 Reorder the terms: 15.75 + -15.75 + 8x + x2 = 0 + -15.75 Combine like terms: 15.75 + -15.75 = 0.00 0.00 + 8x + x2 = 0 + -15.75 8x + x2 = 0 + -15.75 Combine like terms: 0 + -15.75 = -15.75 8x + x2 = -15.75 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 = -15.75 + 16 Reorder the terms: 16 + 8x + x2 = -15.75 + 16 Combine like terms: -15.75 + 16 = 0.25 16 + 8x + x2 = 0.25 Factor a perfect square on the left side: (x + 4)(x + 4) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (x + 4) equal to 0.5 and -0.5.Subproblem 1
x + 4 = 0.5 Simplifying x + 4 = 0.5 Reorder the terms: 4 + x = 0.5 Solving 4 + x = 0.5 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 = 0.5 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0.5 + -4 x = 0.5 + -4 Combine like terms: 0.5 + -4 = -3.5 x = -3.5 Simplifying x = -3.5Subproblem 2
x + 4 = -0.5 Simplifying x + 4 = -0.5 Reorder the terms: 4 + x = -0.5 Solving 4 + x = -0.5 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 = -0.5 + -4 Combine like terms: 4 + -4 = 0 0 + x = -0.5 + -4 x = -0.5 + -4 Combine like terms: -0.5 + -4 = -4.5 x = -4.5 Simplifying x = -4.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.5, -4.5}
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