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Simplifying x2 + 5x = 172 Reorder the terms: 5x + x2 = 172 Solving 5x + x2 = 172 Solving for variable 'x'. Reorder the terms: -172 + 5x + x2 = 172 + -172 Combine like terms: 172 + -172 = 0 -172 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '172' to each side of the equation. -172 + 5x + 172 + x2 = 0 + 172 Reorder the terms: -172 + 172 + 5x + x2 = 0 + 172 Combine like terms: -172 + 172 = 0 0 + 5x + x2 = 0 + 172 5x + x2 = 0 + 172 Combine like terms: 0 + 172 = 172 5x + x2 = 172 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 = 172 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 172 + 6.25 Combine like terms: 172 + 6.25 = 178.25 6.25 + 5x + x2 = 178.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 178.25 Calculate the square root of the right side: 13.351029923 Break this problem into two subproblems by setting (x + 2.5) equal to 13.351029923 and -13.351029923.Subproblem 1
x + 2.5 = 13.351029923 Simplifying x + 2.5 = 13.351029923 Reorder the terms: 2.5 + x = 13.351029923 Solving 2.5 + x = 13.351029923 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 = 13.351029923 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 13.351029923 + -2.5 x = 13.351029923 + -2.5 Combine like terms: 13.351029923 + -2.5 = 10.851029923 x = 10.851029923 Simplifying x = 10.851029923Subproblem 2
x + 2.5 = -13.351029923 Simplifying x + 2.5 = -13.351029923 Reorder the terms: 2.5 + x = -13.351029923 Solving 2.5 + x = -13.351029923 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 = -13.351029923 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -13.351029923 + -2.5 x = -13.351029923 + -2.5 Combine like terms: -13.351029923 + -2.5 = -15.851029923 x = -15.851029923 Simplifying x = -15.851029923Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.851029923, -15.851029923}
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