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Simplifying x2 + -2x = 37 Reorder the terms: -2x + x2 = 37 Solving -2x + x2 = 37 Solving for variable 'x'. Reorder the terms: -37 + -2x + x2 = 37 + -37 Combine like terms: 37 + -37 = 0 -37 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '37' to each side of the equation. -37 + -2x + 37 + x2 = 0 + 37 Reorder the terms: -37 + 37 + -2x + x2 = 0 + 37 Combine like terms: -37 + 37 = 0 0 + -2x + x2 = 0 + 37 -2x + x2 = 0 + 37 Combine like terms: 0 + 37 = 37 -2x + x2 = 37 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 = 37 + 1 Reorder the terms: 1 + -2x + x2 = 37 + 1 Combine like terms: 37 + 1 = 38 1 + -2x + x2 = 38 Factor a perfect square on the left side: (x + -1)(x + -1) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (x + -1) equal to 6.164414003 and -6.164414003.Subproblem 1
x + -1 = 6.164414003 Simplifying x + -1 = 6.164414003 Reorder the terms: -1 + x = 6.164414003 Solving -1 + x = 6.164414003 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 = 6.164414003 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.164414003 + 1 x = 6.164414003 + 1 Combine like terms: 6.164414003 + 1 = 7.164414003 x = 7.164414003 Simplifying x = 7.164414003Subproblem 2
x + -1 = -6.164414003 Simplifying x + -1 = -6.164414003 Reorder the terms: -1 + x = -6.164414003 Solving -1 + x = -6.164414003 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 = -6.164414003 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.164414003 + 1 x = -6.164414003 + 1 Combine like terms: -6.164414003 + 1 = -5.164414003 x = -5.164414003 Simplifying x = -5.164414003Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.164414003, -5.164414003}
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