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Simplifying x2 + -2x + 1 = 75 Reorder the terms: 1 + -2x + x2 = 75 Solving 1 + -2x + x2 = 75 Solving for variable 'x'. Reorder the terms: 1 + -75 + -2x + x2 = 75 + -75 Combine like terms: 1 + -75 = -74 -74 + -2x + x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -74 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '74' to each side of the equation. -74 + -2x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + -2x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -2x + x2 = 0 + 74 -2x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 -2x + x2 = 74 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 74 + 1 Reorder the terms: 1 + -2x + x2 = 74 + 1 Combine like terms: 74 + 1 = 75 1 + -2x + x2 = 75 Factor a perfect square on the left side: (x + -1)(x + -1) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (x + -1) equal to 8.660254038 and -8.660254038.Subproblem 1
x + -1 = 8.660254038 Simplifying x + -1 = 8.660254038 Reorder the terms: -1 + x = 8.660254038 Solving -1 + x = 8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 8.660254038 + 1 Combine like terms: -1 + 1 = 0 0 + x = 8.660254038 + 1 x = 8.660254038 + 1 Combine like terms: 8.660254038 + 1 = 9.660254038 x = 9.660254038 Simplifying x = 9.660254038Subproblem 2
x + -1 = -8.660254038 Simplifying x + -1 = -8.660254038 Reorder the terms: -1 + x = -8.660254038 Solving -1 + x = -8.660254038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -8.660254038 + 1 Combine like terms: -1 + 1 = 0 0 + x = -8.660254038 + 1 x = -8.660254038 + 1 Combine like terms: -8.660254038 + 1 = -7.660254038 x = -7.660254038 Simplifying x = -7.660254038Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.660254038, -7.660254038}
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