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Simplifying x2 + 5x = 29 Reorder the terms: 5x + x2 = 29 Solving 5x + x2 = 29 Solving for variable 'x'. Reorder the terms: -29 + 5x + x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 5x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + 5x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 5x + x2 = 0 + 29 5x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 5x + x2 = 29 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 = 29 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 29 + 6.25 Combine like terms: 29 + 6.25 = 35.25 6.25 + 5x + x2 = 35.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 35.25 Calculate the square root of the right side: 5.937171044 Break this problem into two subproblems by setting (x + 2.5) equal to 5.937171044 and -5.937171044.Subproblem 1
x + 2.5 = 5.937171044 Simplifying x + 2.5 = 5.937171044 Reorder the terms: 2.5 + x = 5.937171044 Solving 2.5 + x = 5.937171044 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 = 5.937171044 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5.937171044 + -2.5 x = 5.937171044 + -2.5 Combine like terms: 5.937171044 + -2.5 = 3.437171044 x = 3.437171044 Simplifying x = 3.437171044Subproblem 2
x + 2.5 = -5.937171044 Simplifying x + 2.5 = -5.937171044 Reorder the terms: 2.5 + x = -5.937171044 Solving 2.5 + x = -5.937171044 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 = -5.937171044 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5.937171044 + -2.5 x = -5.937171044 + -2.5 Combine like terms: -5.937171044 + -2.5 = -8.437171044 x = -8.437171044 Simplifying x = -8.437171044Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.437171044, -8.437171044}
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