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Simplifying x2 + -10x + 25 = 54 Reorder the terms: 25 + -10x + x2 = 54 Solving 25 + -10x + x2 = 54 Solving for variable 'x'. Reorder the terms: 25 + -54 + -10x + x2 = 54 + -54 Combine like terms: 25 + -54 = -29 -29 + -10x + x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -29 + -10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -10x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -10x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -10x + x2 = 0 + 29 -10x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -10x + x2 = 29 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 = 29 + 25 Reorder the terms: 25 + -10x + x2 = 29 + 25 Combine like terms: 29 + 25 = 54 25 + -10x + x2 = 54 Factor a perfect square on the left side: (x + -5)(x + -5) = 54 Calculate the square root of the right side: 7.348469228 Break this problem into two subproblems by setting (x + -5) equal to 7.348469228 and -7.348469228.Subproblem 1
x + -5 = 7.348469228 Simplifying x + -5 = 7.348469228 Reorder the terms: -5 + x = 7.348469228 Solving -5 + x = 7.348469228 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 = 7.348469228 + 5 Combine like terms: -5 + 5 = 0 0 + x = 7.348469228 + 5 x = 7.348469228 + 5 Combine like terms: 7.348469228 + 5 = 12.348469228 x = 12.348469228 Simplifying x = 12.348469228Subproblem 2
x + -5 = -7.348469228 Simplifying x + -5 = -7.348469228 Reorder the terms: -5 + x = -7.348469228 Solving -5 + x = -7.348469228 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 = -7.348469228 + 5 Combine like terms: -5 + 5 = 0 0 + x = -7.348469228 + 5 x = -7.348469228 + 5 Combine like terms: -7.348469228 + 5 = -2.348469228 x = -2.348469228 Simplifying x = -2.348469228Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.348469228, -2.348469228}
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