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Simplifying x2 + 42x = 175 Reorder the terms: 42x + x2 = 175 Solving 42x + x2 = 175 Solving for variable 'x'. Reorder the terms: -175 + 42x + x2 = 175 + -175 Combine like terms: 175 + -175 = 0 -175 + 42x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '175' to each side of the equation. -175 + 42x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + 42x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + 42x + x2 = 0 + 175 42x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 42x + x2 = 175 The x term is 42x. Take half its coefficient (21). Square it (441) and add it to both sides. Add '441' to each side of the equation. 42x + 441 + x2 = 175 + 441 Reorder the terms: 441 + 42x + x2 = 175 + 441 Combine like terms: 175 + 441 = 616 441 + 42x + x2 = 616 Factor a perfect square on the left side: (x + 21)(x + 21) = 616 Calculate the square root of the right side: 24.819347292 Break this problem into two subproblems by setting (x + 21) equal to 24.819347292 and -24.819347292.Subproblem 1
x + 21 = 24.819347292 Simplifying x + 21 = 24.819347292 Reorder the terms: 21 + x = 24.819347292 Solving 21 + x = 24.819347292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = 24.819347292 + -21 Combine like terms: 21 + -21 = 0 0 + x = 24.819347292 + -21 x = 24.819347292 + -21 Combine like terms: 24.819347292 + -21 = 3.819347292 x = 3.819347292 Simplifying x = 3.819347292Subproblem 2
x + 21 = -24.819347292 Simplifying x + 21 = -24.819347292 Reorder the terms: 21 + x = -24.819347292 Solving 21 + x = -24.819347292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = -24.819347292 + -21 Combine like terms: 21 + -21 = 0 0 + x = -24.819347292 + -21 x = -24.819347292 + -21 Combine like terms: -24.819347292 + -21 = -45.819347292 x = -45.819347292 Simplifying x = -45.819347292Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.819347292, -45.819347292}
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