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Simplifying x(x + 1) = 675 Reorder the terms: x(1 + x) = 675 (1 * x + x * x) = 675 (1x + x2) = 675 Solving 1x + x2 = 675 Solving for variable 'x'. Reorder the terms: -675 + 1x + x2 = 675 + -675 Combine like terms: 675 + -675 = 0 -675 + 1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '675' to each side of the equation. -675 + 1x + 675 + x2 = 0 + 675 Reorder the terms: -675 + 675 + 1x + x2 = 0 + 675 Combine like terms: -675 + 675 = 0 0 + 1x + x2 = 0 + 675 1x + x2 = 0 + 675 Combine like terms: 0 + 675 = 675 1x + x2 = 675 The x term is 1x. 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 = 675 + 0.25 Reorder the terms: 0.25 + x + x2 = 675 + 0.25 Combine like terms: 675 + 0.25 = 675.25 0.25 + x + x2 = 675.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 675.25 Calculate the square root of the right side: 25.98557292 Break this problem into two subproblems by setting (x + 0.5) equal to 25.98557292 and -25.98557292.Subproblem 1
x + 0.5 = 25.98557292 Simplifying x + 0.5 = 25.98557292 Reorder the terms: 0.5 + x = 25.98557292 Solving 0.5 + x = 25.98557292 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 = 25.98557292 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 25.98557292 + -0.5 x = 25.98557292 + -0.5 Combine like terms: 25.98557292 + -0.5 = 25.48557292 x = 25.48557292 Simplifying x = 25.48557292Subproblem 2
x + 0.5 = -25.98557292 Simplifying x + 0.5 = -25.98557292 Reorder the terms: 0.5 + x = -25.98557292 Solving 0.5 + x = -25.98557292 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 = -25.98557292 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -25.98557292 + -0.5 x = -25.98557292 + -0.5 Combine like terms: -25.98557292 + -0.5 = -26.48557292 x = -26.48557292 Simplifying x = -26.48557292Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.48557292, -26.48557292}
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