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Simplifying 0.5x2 + 6x + 10 = 0 Reorder the terms: 10 + 6x + 0.5x2 = 0 Solving 10 + 6x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 20 + 12x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + 12x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 12x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 12x + x2 = 0 + -20 12x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 12x + x2 = -20 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 = -20 + 36 Reorder the terms: 36 + 12x + x2 = -20 + 36 Combine like terms: -20 + 36 = 16 36 + 12x + x2 = 16 Factor a perfect square on the left side: (x + 6)(x + 6) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + 6) equal to 4 and -4.Subproblem 1
x + 6 = 4 Simplifying x + 6 = 4 Reorder the terms: 6 + x = 4 Solving 6 + x = 4 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 = 4 + -6 Combine like terms: 6 + -6 = 0 0 + x = 4 + -6 x = 4 + -6 Combine like terms: 4 + -6 = -2 x = -2 Simplifying x = -2Subproblem 2
x + 6 = -4 Simplifying x + 6 = -4 Reorder the terms: 6 + x = -4 Solving 6 + x = -4 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 = -4 + -6 Combine like terms: 6 + -6 = 0 0 + x = -4 + -6 x = -4 + -6 Combine like terms: -4 + -6 = -10 x = -10 Simplifying x = -10Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2, -10}
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