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Simplifying 2x(x + 4) + 3.5 = 0 Reorder the terms: 2x(4 + x) + 3.5 = 0 (4 * 2x + x * 2x) + 3.5 = 0 (8x + 2x2) + 3.5 = 0 Reorder the terms: 3.5 + 8x + 2x2 = 0 Solving 3.5 + 8x + 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'. 1.75 + 4x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + 4x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + 4x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + 4x + x2 = 0 + -1.75 4x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 4x + x2 = -1.75 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -1.75 + 4 Reorder the terms: 4 + 4x + x2 = -1.75 + 4 Combine like terms: -1.75 + 4 = 2.25 4 + 4x + x2 = 2.25 Factor a perfect square on the left side: (x + 2)(x + 2) = 2.25 Calculate the square root of the right side: 1.5 Break this problem into two subproblems by setting (x + 2) equal to 1.5 and -1.5.Subproblem 1
x + 2 = 1.5 Simplifying x + 2 = 1.5 Reorder the terms: 2 + x = 1.5 Solving 2 + x = 1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.5 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.5 + -2 x = 1.5 + -2 Combine like terms: 1.5 + -2 = -0.5 x = -0.5 Simplifying x = -0.5Subproblem 2
x + 2 = -1.5 Simplifying x + 2 = -1.5 Reorder the terms: 2 + x = -1.5 Solving 2 + x = -1.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.5 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.5 + -2 x = -1.5 + -2 Combine like terms: -1.5 + -2 = -3.5 x = -3.5 Simplifying x = -3.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.5, -3.5}
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