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Simplifying x2 + x + 5 = 625 Reorder the terms: 5 + x + x2 = 625 Solving 5 + x + x2 = 625 Solving for variable 'x'. Reorder the terms: 5 + -625 + x + x2 = 625 + -625 Combine like terms: 5 + -625 = -620 -620 + x + x2 = 625 + -625 Combine like terms: 625 + -625 = 0 -620 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '620' to each side of the equation. -620 + x + 620 + x2 = 0 + 620 Reorder the terms: -620 + 620 + x + x2 = 0 + 620 Combine like terms: -620 + 620 = 0 0 + x + x2 = 0 + 620 x + x2 = 0 + 620 Combine like terms: 0 + 620 = 620 x + x2 = 620 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 620 + 0.25 Reorder the terms: 0.25 + x + x2 = 620 + 0.25 Combine like terms: 620 + 0.25 = 620.25 0.25 + x + x2 = 620.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 620.25 Calculate the square root of the right side: 24.904818811 Break this problem into two subproblems by setting (x + 0.5) equal to 24.904818811 and -24.904818811.Subproblem 1
x + 0.5 = 24.904818811 Simplifying x + 0.5 = 24.904818811 Reorder the terms: 0.5 + x = 24.904818811 Solving 0.5 + x = 24.904818811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 24.904818811 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 24.904818811 + -0.5 x = 24.904818811 + -0.5 Combine like terms: 24.904818811 + -0.5 = 24.404818811 x = 24.404818811 Simplifying x = 24.404818811Subproblem 2
x + 0.5 = -24.904818811 Simplifying x + 0.5 = -24.904818811 Reorder the terms: 0.5 + x = -24.904818811 Solving 0.5 + x = -24.904818811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -24.904818811 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -24.904818811 + -0.5 x = -24.904818811 + -0.5 Combine like terms: -24.904818811 + -0.5 = -25.404818811 x = -25.404818811 Simplifying x = -25.404818811Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.404818811, -25.404818811}
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