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Simplifying x(x + -5) = 120 Reorder the terms: x(-5 + x) = 120 (-5 * x + x * x) = 120 (-5x + x2) = 120 Solving -5x + x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + -5x + x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + -5x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -5x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -5x + x2 = 0 + 120 -5x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -5x + x2 = 120 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 120 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 120 + 6.25 Combine like terms: 120 + 6.25 = 126.25 6.25 + -5x + x2 = 126.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (x + -2.5) equal to 11.236102527 and -11.236102527.Subproblem 1
x + -2.5 = 11.236102527 Simplifying x + -2.5 = 11.236102527 Reorder the terms: -2.5 + x = 11.236102527 Solving -2.5 + x = 11.236102527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 11.236102527 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 11.236102527 + 2.5 x = 11.236102527 + 2.5 Combine like terms: 11.236102527 + 2.5 = 13.736102527 x = 13.736102527 Simplifying x = 13.736102527Subproblem 2
x + -2.5 = -11.236102527 Simplifying x + -2.5 = -11.236102527 Reorder the terms: -2.5 + x = -11.236102527 Solving -2.5 + x = -11.236102527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -11.236102527 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -11.236102527 + 2.5 x = -11.236102527 + 2.5 Combine like terms: -11.236102527 + 2.5 = -8.736102527 x = -8.736102527 Simplifying x = -8.736102527Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.736102527, -8.736102527}
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