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Simplifying 36 = 0.5x(x + -5) Reorder the terms: 36 = 0.5x(-5 + x) 36 = (-5 * 0.5x + x * 0.5x) 36 = (-2.5x + 0.5x2) Solving 36 = -2.5x + 0.5x2 Solving for variable 'x'. Reorder the terms: 36 + 2.5x + -0.5x2 = -2.5x + 2.5x + 0.5x2 + -0.5x2 Combine like terms: -2.5x + 2.5x = 0.0 36 + 2.5x + -0.5x2 = 0.0 + 0.5x2 + -0.5x2 36 + 2.5x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 36 + 2.5x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -72 + -5x + x2 = 0 Move the constant term to the right: Add '72' to each side of the equation. -72 + -5x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -5x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -5x + x2 = 0 + 72 -5x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -5x + x2 = 72 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 = 72 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 72 + 6.25 Combine like terms: 72 + 6.25 = 78.25 6.25 + -5x + x2 = 78.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x + -2.5) equal to 8.845903006 and -8.845903006.Subproblem 1
x + -2.5 = 8.845903006 Simplifying x + -2.5 = 8.845903006 Reorder the terms: -2.5 + x = 8.845903006 Solving -2.5 + x = 8.845903006 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 = 8.845903006 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 8.845903006 + 2.5 x = 8.845903006 + 2.5 Combine like terms: 8.845903006 + 2.5 = 11.345903006 x = 11.345903006 Simplifying x = 11.345903006Subproblem 2
x + -2.5 = -8.845903006 Simplifying x + -2.5 = -8.845903006 Reorder the terms: -2.5 + x = -8.845903006 Solving -2.5 + x = -8.845903006 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 = -8.845903006 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -8.845903006 + 2.5 x = -8.845903006 + 2.5 Combine like terms: -8.845903006 + 2.5 = -6.345903006 x = -6.345903006 Simplifying x = -6.345903006Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.345903006, -6.345903006}
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