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Simplifying x2 + 12x + -6.25 = 0 Reorder the terms: -6.25 + 12x + x2 = 0 Solving -6.25 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 12x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 12x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 12x + x2 = 0 + 6.25 12x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 12x + x2 = 6.25 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 6.25 + 36 Reorder the terms: 36 + 12x + x2 = 6.25 + 36 Combine like terms: 6.25 + 36 = 42.25 36 + 12x + x2 = 42.25 Factor a perfect square on the left side: (x + 6)(x + 6) = 42.25 Calculate the square root of the right side: 6.5 Break this problem into two subproblems by setting (x + 6) equal to 6.5 and -6.5.Subproblem 1
x + 6 = 6.5 Simplifying x + 6 = 6.5 Reorder the terms: 6 + x = 6.5 Solving 6 + x = 6.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.5 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.5 + -6 x = 6.5 + -6 Combine like terms: 6.5 + -6 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 6 = -6.5 Simplifying x + 6 = -6.5 Reorder the terms: 6 + x = -6.5 Solving 6 + x = -6.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.5 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.5 + -6 x = -6.5 + -6 Combine like terms: -6.5 + -6 = -12.5 x = -12.5 Simplifying x = -12.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -12.5}
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