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Simplifying -3(x + 2)(x + -0.5) = 0 Reorder the terms: -3(2 + x)(x + -0.5) = 0 Reorder the terms: -3(2 + x)(-0.5 + x) = 0 Multiply (2 + x) * (-0.5 + x) -3(2(-0.5 + x) + x(-0.5 + x)) = 0 -3((-0.5 * 2 + x * 2) + x(-0.5 + x)) = 0 -3((-1 + 2x) + x(-0.5 + x)) = 0 -3(-1 + 2x + (-0.5 * x + x * x)) = 0 -3(-1 + 2x + (-0.5x + x2)) = 0 Combine like terms: 2x + -0.5x = 1.5x -3(-1 + 1.5x + x2) = 0 (-1 * -3 + 1.5x * -3 + x2 * -3) = 0 (3 + -4.5x + -3x2) = 0 Solving 3 + -4.5x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1 + 1.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.5x + x2 = 0 + 1 1.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.5x + x2 = 1 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 1 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 1 + 0.5625 Combine like terms: 1 + 0.5625 = 1.5625 0.5625 + 1.5x + x2 = 1.5625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 1.5625 Calculate the square root of the right side: 1.25 Break this problem into two subproblems by setting (x + 0.75) equal to 1.25 and -1.25.Subproblem 1
x + 0.75 = 1.25 Simplifying x + 0.75 = 1.25 Reorder the terms: 0.75 + x = 1.25 Solving 0.75 + x = 1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 1.25 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 1.25 + -0.75 x = 1.25 + -0.75 Combine like terms: 1.25 + -0.75 = 0.5 x = 0.5 Simplifying x = 0.5Subproblem 2
x + 0.75 = -1.25 Simplifying x + 0.75 = -1.25 Reorder the terms: 0.75 + x = -1.25 Solving 0.75 + x = -1.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -1.25 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -1.25 + -0.75 x = -1.25 + -0.75 Combine like terms: -1.25 + -0.75 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5, -2}
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