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Simplifying x2 + -10x + 25 = 51 Reorder the terms: 25 + -10x + x2 = 51 Solving 25 + -10x + x2 = 51 Solving for variable 'x'. Reorder the terms: 25 + -51 + -10x + x2 = 51 + -51 Combine like terms: 25 + -51 = -26 -26 + -10x + x2 = 51 + -51 Combine like terms: 51 + -51 = 0 -26 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -10x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -10x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -10x + x2 = 0 + 26 -10x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -10x + x2 = 26 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 26 + 25 Reorder the terms: 25 + -10x + x2 = 26 + 25 Combine like terms: 26 + 25 = 51 25 + -10x + x2 = 51 Factor a perfect square on the left side: (x + -5)(x + -5) = 51 Calculate the square root of the right side: 7.141428429 Break this problem into two subproblems by setting (x + -5) equal to 7.141428429 and -7.141428429.Subproblem 1
x + -5 = 7.141428429 Simplifying x + -5 = 7.141428429 Reorder the terms: -5 + x = 7.141428429 Solving -5 + x = 7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 7.141428429 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.141428429 + 5 x = 7.141428429 + 5 Combine like terms: 7.141428429 + 5 = 12.141428429 x = 12.141428429 Simplifying x = 12.141428429Subproblem 2
x + -5 = -7.141428429 Simplifying x + -5 = -7.141428429 Reorder the terms: -5 + x = -7.141428429 Solving -5 + x = -7.141428429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -7.141428429 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.141428429 + 5 x = -7.141428429 + 5 Combine like terms: -7.141428429 + 5 = -2.141428429 x = -2.141428429 Simplifying x = -2.141428429Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.141428429, -2.141428429}
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