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Simplifying x2 + -25x + 76 = 0 Reorder the terms: 76 + -25x + x2 = 0 Solving 76 + -25x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-76' to each side of the equation. 76 + -25x + -76 + x2 = 0 + -76 Reorder the terms: 76 + -76 + -25x + x2 = 0 + -76 Combine like terms: 76 + -76 = 0 0 + -25x + x2 = 0 + -76 -25x + x2 = 0 + -76 Combine like terms: 0 + -76 = -76 -25x + x2 = -76 The x term is -25x. Take half its coefficient (-12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. -25x + 156.25 + x2 = -76 + 156.25 Reorder the terms: 156.25 + -25x + x2 = -76 + 156.25 Combine like terms: -76 + 156.25 = 80.25 156.25 + -25x + x2 = 80.25 Factor a perfect square on the left side: (x + -12.5)(x + -12.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (x + -12.5) equal to 8.958236434 and -8.958236434.Subproblem 1
x + -12.5 = 8.958236434 Simplifying x + -12.5 = 8.958236434 Reorder the terms: -12.5 + x = 8.958236434 Solving -12.5 + x = 8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 8.958236434 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 8.958236434 + 12.5 x = 8.958236434 + 12.5 Combine like terms: 8.958236434 + 12.5 = 21.458236434 x = 21.458236434 Simplifying x = 21.458236434Subproblem 2
x + -12.5 = -8.958236434 Simplifying x + -12.5 = -8.958236434 Reorder the terms: -12.5 + x = -8.958236434 Solving -12.5 + x = -8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -8.958236434 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -8.958236434 + 12.5 x = -8.958236434 + 12.5 Combine like terms: -8.958236434 + 12.5 = 3.541763566 x = 3.541763566 Simplifying x = 3.541763566Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.458236434, 3.541763566}
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