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Simplifying x(x + -4) = 2.25 Reorder the terms: x(-4 + x) = 2.25 (-4 * x + x * x) = 2.25 (-4x + x2) = 2.25 Solving -4x + x2 = 2.25 Solving for variable 'x'. Reorder the terms: -2.25 + -4x + x2 = 2.25 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 -2.25 + -4x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -4x + 2.25 + x2 = 0.00 + 2.25 Reorder the terms: -2.25 + 2.25 + -4x + x2 = 0.00 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -4x + x2 = 0.00 + 2.25 -4x + x2 = 0.00 + 2.25 Combine like terms: 0.00 + 2.25 = 2.25 -4x + x2 = 2.25 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 2.25 + 4 Reorder the terms: 4 + -4x + x2 = 2.25 + 4 Combine like terms: 2.25 + 4 = 6.25 4 + -4x + x2 = 6.25 Factor a perfect square on the left side: (x + -2)(x + -2) = 6.25 Calculate the square root of the right side: 2.5 Break this problem into two subproblems by setting (x + -2) equal to 2.5 and -2.5.Subproblem 1
x + -2 = 2.5 Simplifying x + -2 = 2.5 Reorder the terms: -2 + x = 2.5 Solving -2 + x = 2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.5 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.5 + 2 x = 2.5 + 2 Combine like terms: 2.5 + 2 = 4.5 x = 4.5 Simplifying x = 4.5Subproblem 2
x + -2 = -2.5 Simplifying x + -2 = -2.5 Reorder the terms: -2 + x = -2.5 Solving -2 + x = -2.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.5 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.5 + 2 x = -2.5 + 2 Combine like terms: -2.5 + 2 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.5, -0.5}
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