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Simplifying x2 + 5x = 342 Reorder the terms: 5x + x2 = 342 Solving 5x + x2 = 342 Solving for variable 'x'. Reorder the terms: -342 + 5x + x2 = 342 + -342 Combine like terms: 342 + -342 = 0 -342 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '342' to each side of the equation. -342 + 5x + 342 + x2 = 0 + 342 Reorder the terms: -342 + 342 + 5x + x2 = 0 + 342 Combine like terms: -342 + 342 = 0 0 + 5x + x2 = 0 + 342 5x + x2 = 0 + 342 Combine like terms: 0 + 342 = 342 5x + x2 = 342 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 = 342 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 342 + 6.25 Combine like terms: 342 + 6.25 = 348.25 6.25 + 5x + x2 = 348.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 348.25 Calculate the square root of the right side: 18.661457607 Break this problem into two subproblems by setting (x + 2.5) equal to 18.661457607 and -18.661457607.Subproblem 1
x + 2.5 = 18.661457607 Simplifying x + 2.5 = 18.661457607 Reorder the terms: 2.5 + x = 18.661457607 Solving 2.5 + x = 18.661457607 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 = 18.661457607 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 18.661457607 + -2.5 x = 18.661457607 + -2.5 Combine like terms: 18.661457607 + -2.5 = 16.161457607 x = 16.161457607 Simplifying x = 16.161457607Subproblem 2
x + 2.5 = -18.661457607 Simplifying x + 2.5 = -18.661457607 Reorder the terms: 2.5 + x = -18.661457607 Solving 2.5 + x = -18.661457607 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 = -18.661457607 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -18.661457607 + -2.5 x = -18.661457607 + -2.5 Combine like terms: -18.661457607 + -2.5 = -21.161457607 x = -21.161457607 Simplifying x = -21.161457607Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.161457607, -21.161457607}
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