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Simplifying x2 + x = 624 Reorder the terms: x + x2 = 624 Solving x + x2 = 624 Solving for variable 'x'. Reorder the terms: -624 + x + x2 = 624 + -624 Combine like terms: 624 + -624 = 0 -624 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '624' to each side of the equation. -624 + x + 624 + x2 = 0 + 624 Reorder the terms: -624 + 624 + x + x2 = 0 + 624 Combine like terms: -624 + 624 = 0 0 + x + x2 = 0 + 624 x + x2 = 0 + 624 Combine like terms: 0 + 624 = 624 x + x2 = 624 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 = 624 + 0.25 Reorder the terms: 0.25 + x + x2 = 624 + 0.25 Combine like terms: 624 + 0.25 = 624.25 0.25 + x + x2 = 624.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 624.25 Calculate the square root of the right side: 24.984995497 Break this problem into two subproblems by setting (x + 0.5) equal to 24.984995497 and -24.984995497.Subproblem 1
x + 0.5 = 24.984995497 Simplifying x + 0.5 = 24.984995497 Reorder the terms: 0.5 + x = 24.984995497 Solving 0.5 + x = 24.984995497 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 = 24.984995497 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 24.984995497 + -0.5 x = 24.984995497 + -0.5 Combine like terms: 24.984995497 + -0.5 = 24.484995497 x = 24.484995497 Simplifying x = 24.484995497Subproblem 2
x + 0.5 = -24.984995497 Simplifying x + 0.5 = -24.984995497 Reorder the terms: 0.5 + x = -24.984995497 Solving 0.5 + x = -24.984995497 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 = -24.984995497 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -24.984995497 + -0.5 x = -24.984995497 + -0.5 Combine like terms: -24.984995497 + -0.5 = -25.484995497 x = -25.484995497 Simplifying x = -25.484995497Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.484995497, -25.484995497}
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