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Simplifying x(x + 5) = 2100 Reorder the terms: x(5 + x) = 2100 (5 * x + x * x) = 2100 (5x + x2) = 2100 Solving 5x + x2 = 2100 Solving for variable 'x'. Reorder the terms: -2100 + 5x + x2 = 2100 + -2100 Combine like terms: 2100 + -2100 = 0 -2100 + 5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2100' to each side of the equation. -2100 + 5x + 2100 + x2 = 0 + 2100 Reorder the terms: -2100 + 2100 + 5x + x2 = 0 + 2100 Combine like terms: -2100 + 2100 = 0 0 + 5x + x2 = 0 + 2100 5x + x2 = 0 + 2100 Combine like terms: 0 + 2100 = 2100 5x + x2 = 2100 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 = 2100 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 2100 + 6.25 Combine like terms: 2100 + 6.25 = 2106.25 6.25 + 5x + x2 = 2106.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 2106.25 Calculate the square root of the right side: 45.893899377 Break this problem into two subproblems by setting (x + 2.5) equal to 45.893899377 and -45.893899377.Subproblem 1
x + 2.5 = 45.893899377 Simplifying x + 2.5 = 45.893899377 Reorder the terms: 2.5 + x = 45.893899377 Solving 2.5 + x = 45.893899377 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 = 45.893899377 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 45.893899377 + -2.5 x = 45.893899377 + -2.5 Combine like terms: 45.893899377 + -2.5 = 43.393899377 x = 43.393899377 Simplifying x = 43.393899377Subproblem 2
x + 2.5 = -45.893899377 Simplifying x + 2.5 = -45.893899377 Reorder the terms: 2.5 + x = -45.893899377 Solving 2.5 + x = -45.893899377 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 = -45.893899377 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -45.893899377 + -2.5 x = -45.893899377 + -2.5 Combine like terms: -45.893899377 + -2.5 = -48.393899377 x = -48.393899377 Simplifying x = -48.393899377Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.393899377, -48.393899377}
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