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Simplifying x2 = -10x + 38 Reorder the terms: x2 = 38 + -10x Solving x2 = 38 + -10x Solving for variable 'x'. Reorder the terms: -38 + 10x + x2 = 38 + -10x + -38 + 10x Reorder the terms: -38 + 10x + x2 = 38 + -38 + -10x + 10x Combine like terms: 38 + -38 = 0 -38 + 10x + x2 = 0 + -10x + 10x -38 + 10x + x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -38 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + 10x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + 10x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + 10x + x2 = 0 + 38 10x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 10x + x2 = 38 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 = 38 + 25 Reorder the terms: 25 + 10x + x2 = 38 + 25 Combine like terms: 38 + 25 = 63 25 + 10x + x2 = 63 Factor a perfect square on the left side: (x + 5)(x + 5) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + 5) equal to 7.937253933 and -7.937253933.Subproblem 1
x + 5 = 7.937253933 Simplifying x + 5 = 7.937253933 Reorder the terms: 5 + x = 7.937253933 Solving 5 + x = 7.937253933 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 = 7.937253933 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.937253933 + -5 x = 7.937253933 + -5 Combine like terms: 7.937253933 + -5 = 2.937253933 x = 2.937253933 Simplifying x = 2.937253933Subproblem 2
x + 5 = -7.937253933 Simplifying x + 5 = -7.937253933 Reorder the terms: 5 + x = -7.937253933 Solving 5 + x = -7.937253933 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 = -7.937253933 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.937253933 + -5 x = -7.937253933 + -5 Combine like terms: -7.937253933 + -5 = -12.937253933 x = -12.937253933 Simplifying x = -12.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.937253933, -12.937253933}
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