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Simplifying x2 + 8x + 2.33 = 0 Reorder the terms: 2.33 + 8x + x2 = 0 Solving 2.33 + 8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2.33' to each side of the equation. 2.33 + 8x + -2.33 + x2 = 0 + -2.33 Reorder the terms: 2.33 + -2.33 + 8x + x2 = 0 + -2.33 Combine like terms: 2.33 + -2.33 = 0.00 0.00 + 8x + x2 = 0 + -2.33 8x + x2 = 0 + -2.33 Combine like terms: 0 + -2.33 = -2.33 8x + x2 = -2.33 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 = -2.33 + 16 Reorder the terms: 16 + 8x + x2 = -2.33 + 16 Combine like terms: -2.33 + 16 = 13.67 16 + 8x + x2 = 13.67 Factor a perfect square on the left side: (x + 4)(x + 4) = 13.67 Calculate the square root of the right side: 3.697296309 Break this problem into two subproblems by setting (x + 4) equal to 3.697296309 and -3.697296309.Subproblem 1
x + 4 = 3.697296309 Simplifying x + 4 = 3.697296309 Reorder the terms: 4 + x = 3.697296309 Solving 4 + x = 3.697296309 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 = 3.697296309 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.697296309 + -4 x = 3.697296309 + -4 Combine like terms: 3.697296309 + -4 = -0.302703691 x = -0.302703691 Simplifying x = -0.302703691Subproblem 2
x + 4 = -3.697296309 Simplifying x + 4 = -3.697296309 Reorder the terms: 4 + x = -3.697296309 Solving 4 + x = -3.697296309 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 = -3.697296309 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.697296309 + -4 x = -3.697296309 + -4 Combine like terms: -3.697296309 + -4 = -7.697296309 x = -7.697296309 Simplifying x = -7.697296309Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.302703691, -7.697296309}
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