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Simplifying x2 + -42x + -7 = 0 Reorder the terms: -7 + -42x + x2 = 0 Solving -7 + -42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -42x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -42x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -42x + x2 = 0 + 7 -42x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -42x + x2 = 7 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 = 7 + 441 Reorder the terms: 441 + -42x + x2 = 7 + 441 Combine like terms: 7 + 441 = 448 441 + -42x + x2 = 448 Factor a perfect square on the left side: (x + -21)(x + -21) = 448 Calculate the square root of the right side: 21.166010489 Break this problem into two subproblems by setting (x + -21) equal to 21.166010489 and -21.166010489.Subproblem 1
x + -21 = 21.166010489 Simplifying x + -21 = 21.166010489 Reorder the terms: -21 + x = 21.166010489 Solving -21 + x = 21.166010489 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 = 21.166010489 + 21 Combine like terms: -21 + 21 = 0 0 + x = 21.166010489 + 21 x = 21.166010489 + 21 Combine like terms: 21.166010489 + 21 = 42.166010489 x = 42.166010489 Simplifying x = 42.166010489Subproblem 2
x + -21 = -21.166010489 Simplifying x + -21 = -21.166010489 Reorder the terms: -21 + x = -21.166010489 Solving -21 + x = -21.166010489 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 = -21.166010489 + 21 Combine like terms: -21 + 21 = 0 0 + x = -21.166010489 + 21 x = -21.166010489 + 21 Combine like terms: -21.166010489 + 21 = -0.166010489 x = -0.166010489 Simplifying x = -0.166010489Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.166010489, -0.166010489}
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