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Simplifying -1x2 + 157x = 42x + 8 Reorder the terms: 157x + -1x2 = 42x + 8 Reorder the terms: 157x + -1x2 = 8 + 42x Solving 157x + -1x2 = 8 + 42x Solving for variable 'x'. Reorder the terms: -8 + 157x + -42x + -1x2 = 8 + 42x + -8 + -42x Combine like terms: 157x + -42x = 115x -8 + 115x + -1x2 = 8 + 42x + -8 + -42x Reorder the terms: -8 + 115x + -1x2 = 8 + -8 + 42x + -42x Combine like terms: 8 + -8 = 0 -8 + 115x + -1x2 = 0 + 42x + -42x -8 + 115x + -1x2 = 42x + -42x Combine like terms: 42x + -42x = 0 -8 + 115x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -115x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -115x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -115x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -115x + x2 = 0 + -8 -115x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -115x + x2 = -8 The x term is -115x. Take half its coefficient (-57.5). Square it (3306.25) and add it to both sides. Add '3306.25' to each side of the equation. -115x + 3306.25 + x2 = -8 + 3306.25 Reorder the terms: 3306.25 + -115x + x2 = -8 + 3306.25 Combine like terms: -8 + 3306.25 = 3298.25 3306.25 + -115x + x2 = 3298.25 Factor a perfect square on the left side: (x + -57.5)(x + -57.5) = 3298.25 Calculate the square root of the right side: 57.430392651 Break this problem into two subproblems by setting (x + -57.5) equal to 57.430392651 and -57.430392651.Subproblem 1
x + -57.5 = 57.430392651 Simplifying x + -57.5 = 57.430392651 Reorder the terms: -57.5 + x = 57.430392651 Solving -57.5 + x = 57.430392651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '57.5' to each side of the equation. -57.5 + 57.5 + x = 57.430392651 + 57.5 Combine like terms: -57.5 + 57.5 = 0.0 0.0 + x = 57.430392651 + 57.5 x = 57.430392651 + 57.5 Combine like terms: 57.430392651 + 57.5 = 114.930392651 x = 114.930392651 Simplifying x = 114.930392651Subproblem 2
x + -57.5 = -57.430392651 Simplifying x + -57.5 = -57.430392651 Reorder the terms: -57.5 + x = -57.430392651 Solving -57.5 + x = -57.430392651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '57.5' to each side of the equation. -57.5 + 57.5 + x = -57.430392651 + 57.5 Combine like terms: -57.5 + 57.5 = 0.0 0.0 + x = -57.430392651 + 57.5 x = -57.430392651 + 57.5 Combine like terms: -57.430392651 + 57.5 = 0.069607349 x = 0.069607349 Simplifying x = 0.069607349Solution
The solution to the problem is based on the solutions from the subproblems. x = {114.930392651, 0.069607349}
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