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Simplifying (x + 2)(x + -1.5) = 0 Reorder the terms: (2 + x)(x + -1.5) = 0 Reorder the terms: (2 + x)(-1.5 + x) = 0 Multiply (2 + x) * (-1.5 + x) (2(-1.5 + x) + x(-1.5 + x)) = 0 ((-1.5 * 2 + x * 2) + x(-1.5 + x)) = 0 ((-3 + 2x) + x(-1.5 + x)) = 0 (-3 + 2x + (-1.5 * x + x * x)) = 0 (-3 + 2x + (-1.5x + x2)) = 0 Combine like terms: 2x + -1.5x = 0.5x (-3 + 0.5x + x2) = 0 Solving -3 + 0.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.5x + x2 = 0 + 3 0.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.5x + x2 = 3 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 3 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 3 + 0.0625 Combine like terms: 3 + 0.0625 = 3.0625 0.0625 + 0.5x + x2 = 3.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 3.0625 Calculate the square root of the right side: 1.75 Break this problem into two subproblems by setting (x + 0.25) equal to 1.75 and -1.75.Subproblem 1
x + 0.25 = 1.75 Simplifying x + 0.25 = 1.75 Reorder the terms: 0.25 + x = 1.75 Solving 0.25 + x = 1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.75 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.75 + -0.25 x = 1.75 + -0.25 Combine like terms: 1.75 + -0.25 = 1.5 x = 1.5 Simplifying x = 1.5Subproblem 2
x + 0.25 = -1.75 Simplifying x + 0.25 = -1.75 Reorder the terms: 0.25 + x = -1.75 Solving 0.25 + x = -1.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.75 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.75 + -0.25 x = -1.75 + -0.25 Combine like terms: -1.75 + -0.25 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5, -2}
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