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Simplifying (x + 2.5)(x + -3) = 0 Reorder the terms: (2.5 + x)(x + -3) = 0 Reorder the terms: (2.5 + x)(-3 + x) = 0 Multiply (2.5 + x) * (-3 + x) (2.5(-3 + x) + x(-3 + x)) = 0 ((-3 * 2.5 + x * 2.5) + x(-3 + x)) = 0 ((-7.5 + 2.5x) + x(-3 + x)) = 0 (-7.5 + 2.5x + (-3 * x + x * x)) = 0 (-7.5 + 2.5x + (-3x + x2)) = 0 Combine like terms: 2.5x + -3x = -0.5x (-7.5 + -0.5x + x2) = 0 Solving -7.5 + -0.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -0.5x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -0.5x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -0.5x + x2 = 0 + 7.5 -0.5x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -0.5x + x2 = 7.5 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 = 7.5 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 7.5 + 0.0625 Combine like terms: 7.5 + 0.0625 = 7.5625 0.0625 + -0.5x + x2 = 7.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 7.5625 Calculate the square root of the right side: 2.75 Break this problem into two subproblems by setting (x + -0.25) equal to 2.75 and -2.75.Subproblem 1
x + -0.25 = 2.75 Simplifying x + -0.25 = 2.75 Reorder the terms: -0.25 + x = 2.75 Solving -0.25 + x = 2.75 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 = 2.75 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.75 + 0.25 x = 2.75 + 0.25 Combine like terms: 2.75 + 0.25 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -0.25 = -2.75 Simplifying x + -0.25 = -2.75 Reorder the terms: -0.25 + x = -2.75 Solving -0.25 + x = -2.75 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 = -2.75 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.75 + 0.25 x = -2.75 + 0.25 Combine like terms: -2.75 + 0.25 = -2.5 x = -2.5 Simplifying x = -2.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, -2.5}
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