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Simplifying 0.2x(x + 3) + -0.4(x + 3) = -0.2x + -0.6 Reorder the terms: 0.2x(3 + x) + -0.4(x + 3) = -0.2x + -0.6 (3 * 0.2x + x * 0.2x) + -0.4(x + 3) = -0.2x + -0.6 (0.6x + 0.2x2) + -0.4(x + 3) = -0.2x + -0.6 Reorder the terms: 0.6x + 0.2x2 + -0.4(3 + x) = -0.2x + -0.6 0.6x + 0.2x2 + (3 * -0.4 + x * -0.4) = -0.2x + -0.6 0.6x + 0.2x2 + (-1.2 + -0.4x) = -0.2x + -0.6 Reorder the terms: -1.2 + 0.6x + -0.4x + 0.2x2 = -0.2x + -0.6 Combine like terms: 0.6x + -0.4x = 0.2x -1.2 + 0.2x + 0.2x2 = -0.2x + -0.6 Reorder the terms: -1.2 + 0.2x + 0.2x2 = -0.6 + -0.2x Solving -1.2 + 0.2x + 0.2x2 = -0.6 + -0.2x Solving for variable 'x'. Reorder the terms: -1.2 + 0.6 + 0.2x + 0.2x + 0.2x2 = -0.6 + -0.2x + 0.6 + 0.2x Combine like terms: -1.2 + 0.6 = -0.6 -0.6 + 0.2x + 0.2x + 0.2x2 = -0.6 + -0.2x + 0.6 + 0.2x Combine like terms: 0.2x + 0.2x = 0.4x -0.6 + 0.4x + 0.2x2 = -0.6 + -0.2x + 0.6 + 0.2x Reorder the terms: -0.6 + 0.4x + 0.2x2 = -0.6 + 0.6 + -0.2x + 0.2x Combine like terms: -0.6 + 0.6 = 0.0 -0.6 + 0.4x + 0.2x2 = 0.0 + -0.2x + 0.2x -0.6 + 0.4x + 0.2x2 = -0.2x + 0.2x Combine like terms: -0.2x + 0.2x = 0.0 -0.6 + 0.4x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -3 + 2x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 2x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 2x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2x + x2 = 0 + 3 2x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 2x + x2 = 3 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 3 + 1 Reorder the terms: 1 + 2x + x2 = 3 + 1 Combine like terms: 3 + 1 = 4 1 + 2x + x2 = 4 Factor a perfect square on the left side: (x + 1)(x + 1) = 4 Calculate the square root of the right side: 2 Break this problem into two subproblems by setting (x + 1) equal to 2 and -2.Subproblem 1
x + 1 = 2 Simplifying x + 1 = 2 Reorder the terms: 1 + x = 2 Solving 1 + x = 2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2 + -1 x = 2 + -1 Combine like terms: 2 + -1 = 1 x = 1 Simplifying x = 1Subproblem 2
x + 1 = -2 Simplifying x + 1 = -2 Reorder the terms: 1 + x = -2 Solving 1 + x = -2 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2 + -1 x = -2 + -1 Combine like terms: -2 + -1 = -3 x = -3 Simplifying x = -3Solution
The solution to the problem is based on the solutions from the subproblems. x = {1, -3}
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