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Simplifying 2x2 + 12x + 17.5 = 0 Reorder the terms: 17.5 + 12x + 2x2 = 0 Solving 17.5 + 12x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 8.75 + 6x + x2 = 0 Move the constant term to the right: Add '-8.75' to each side of the equation. 8.75 + 6x + -8.75 + x2 = 0 + -8.75 Reorder the terms: 8.75 + -8.75 + 6x + x2 = 0 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + 6x + x2 = 0 + -8.75 6x + x2 = 0 + -8.75 Combine like terms: 0 + -8.75 = -8.75 6x + x2 = -8.75 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = -8.75 + 9 Reorder the terms: 9 + 6x + x2 = -8.75 + 9 Combine like terms: -8.75 + 9 = 0.25 9 + 6x + x2 = 0.25 Factor a perfect square on the left side: (x + 3)(x + 3) = 0.25 Calculate the square root of the right side: 0.5 Break this problem into two subproblems by setting (x + 3) equal to 0.5 and -0.5.Subproblem 1
x + 3 = 0.5 Simplifying x + 3 = 0.5 Reorder the terms: 3 + x = 0.5 Solving 3 + x = 0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0.5 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0.5 + -3 x = 0.5 + -3 Combine like terms: 0.5 + -3 = -2.5 x = -2.5 Simplifying x = -2.5Subproblem 2
x + 3 = -0.5 Simplifying x + 3 = -0.5 Reorder the terms: 3 + x = -0.5 Solving 3 + x = -0.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -0.5 + -3 Combine like terms: 3 + -3 = 0 0 + x = -0.5 + -3 x = -0.5 + -3 Combine like terms: -0.5 + -3 = -3.5 x = -3.5 Simplifying x = -3.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.5, -3.5}
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