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Simplifying (x + 0.5)(x + -4) = 0 Reorder the terms: (0.5 + x)(x + -4) = 0 Reorder the terms: (0.5 + x)(-4 + x) = 0 Multiply (0.5 + x) * (-4 + x) (0.5(-4 + x) + x(-4 + x)) = 0 ((-4 * 0.5 + x * 0.5) + x(-4 + x)) = 0 ((-2 + 0.5x) + x(-4 + x)) = 0 (-2 + 0.5x + (-4 * x + x * x)) = 0 (-2 + 0.5x + (-4x + x2)) = 0 Combine like terms: 0.5x + -4x = -3.5x (-2 + -3.5x + x2) = 0 Solving -2 + -3.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -3.5x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -3.5x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3.5x + x2 = 0 + 2 -3.5x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -3.5x + x2 = 2 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 2 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 2 + 3.0625 Combine like terms: 2 + 3.0625 = 5.0625 3.0625 + -3.5x + x2 = 5.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 5.0625 Calculate the square root of the right side: 2.25 Break this problem into two subproblems by setting (x + -1.75) equal to 2.25 and -2.25.Subproblem 1
x + -1.75 = 2.25 Simplifying x + -1.75 = 2.25 Reorder the terms: -1.75 + x = 2.25 Solving -1.75 + x = 2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 2.25 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.25 + 1.75 x = 2.25 + 1.75 Combine like terms: 2.25 + 1.75 = 4 x = 4 Simplifying x = 4Subproblem 2
x + -1.75 = -2.25 Simplifying x + -1.75 = -2.25 Reorder the terms: -1.75 + x = -2.25 Solving -1.75 + x = -2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -2.25 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.25 + 1.75 x = -2.25 + 1.75 Combine like terms: -2.25 + 1.75 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, -0.5}
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