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Simplifying 140 = x2 + 5x Reorder the terms: 140 = 5x + x2 Solving 140 = 5x + x2 Solving for variable 'x'. Reorder the terms: 140 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 140 + -5x + -1x2 = 0 + x2 + -1x2 140 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 140 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -140 + 5x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + 5x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 5x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 5x + x2 = 0 + 140 5x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 5x + x2 = 140 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 = 140 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 140 + 6.25 Combine like terms: 140 + 6.25 = 146.25 6.25 + 5x + x2 = 146.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 146.25 Calculate the square root of the right side: 12.093386622 Break this problem into two subproblems by setting (x + 2.5) equal to 12.093386622 and -12.093386622.Subproblem 1
x + 2.5 = 12.093386622 Simplifying x + 2.5 = 12.093386622 Reorder the terms: 2.5 + x = 12.093386622 Solving 2.5 + x = 12.093386622 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 = 12.093386622 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 12.093386622 + -2.5 x = 12.093386622 + -2.5 Combine like terms: 12.093386622 + -2.5 = 9.593386622 x = 9.593386622 Simplifying x = 9.593386622Subproblem 2
x + 2.5 = -12.093386622 Simplifying x + 2.5 = -12.093386622 Reorder the terms: 2.5 + x = -12.093386622 Solving 2.5 + x = -12.093386622 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 = -12.093386622 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -12.093386622 + -2.5 x = -12.093386622 + -2.5 Combine like terms: -12.093386622 + -2.5 = -14.593386622 x = -14.593386622 Simplifying x = -14.593386622Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.593386622, -14.593386622}
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