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Simplifying x2 + 5x = 504 Reorder the terms: 5x + x2 = 504 Solving 5x + x2 = 504 Solving for variable 'x'. Reorder the terms: -504 + 5x + x2 = 504 + -504 Combine like terms: 504 + -504 = 0 -504 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '504' to each side of the equation. -504 + 5x + 504 + x2 = 0 + 504 Reorder the terms: -504 + 504 + 5x + x2 = 0 + 504 Combine like terms: -504 + 504 = 0 0 + 5x + x2 = 0 + 504 5x + x2 = 0 + 504 Combine like terms: 0 + 504 = 504 5x + x2 = 504 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 = 504 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 504 + 6.25 Combine like terms: 504 + 6.25 = 510.25 6.25 + 5x + x2 = 510.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 510.25 Calculate the square root of the right side: 22.588713996 Break this problem into two subproblems by setting (x + 2.5) equal to 22.588713996 and -22.588713996.Subproblem 1
x + 2.5 = 22.588713996 Simplifying x + 2.5 = 22.588713996 Reorder the terms: 2.5 + x = 22.588713996 Solving 2.5 + x = 22.588713996 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 = 22.588713996 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 22.588713996 + -2.5 x = 22.588713996 + -2.5 Combine like terms: 22.588713996 + -2.5 = 20.088713996 x = 20.088713996 Simplifying x = 20.088713996Subproblem 2
x + 2.5 = -22.588713996 Simplifying x + 2.5 = -22.588713996 Reorder the terms: 2.5 + x = -22.588713996 Solving 2.5 + x = -22.588713996 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 = -22.588713996 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -22.588713996 + -2.5 x = -22.588713996 + -2.5 Combine like terms: -22.588713996 + -2.5 = -25.088713996 x = -25.088713996 Simplifying x = -25.088713996Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.088713996, -25.088713996}
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