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Simplifying x2 + -308x + 3136 = 0 Reorder the terms: 3136 + -308x + x2 = 0 Solving 3136 + -308x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3136' to each side of the equation. 3136 + -308x + -3136 + x2 = 0 + -3136 Reorder the terms: 3136 + -3136 + -308x + x2 = 0 + -3136 Combine like terms: 3136 + -3136 = 0 0 + -308x + x2 = 0 + -3136 -308x + x2 = 0 + -3136 Combine like terms: 0 + -3136 = -3136 -308x + x2 = -3136 The x term is -308x. Take half its coefficient (-154). Square it (23716) and add it to both sides. Add '23716' to each side of the equation. -308x + 23716 + x2 = -3136 + 23716 Reorder the terms: 23716 + -308x + x2 = -3136 + 23716 Combine like terms: -3136 + 23716 = 20580 23716 + -308x + x2 = 20580 Factor a perfect square on the left side: (x + -154)(x + -154) = 20580 Calculate the square root of the right side: 143.457310723 Break this problem into two subproblems by setting (x + -154) equal to 143.457310723 and -143.457310723.Subproblem 1
x + -154 = 143.457310723 Simplifying x + -154 = 143.457310723 Reorder the terms: -154 + x = 143.457310723 Solving -154 + x = 143.457310723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '154' to each side of the equation. -154 + 154 + x = 143.457310723 + 154 Combine like terms: -154 + 154 = 0 0 + x = 143.457310723 + 154 x = 143.457310723 + 154 Combine like terms: 143.457310723 + 154 = 297.457310723 x = 297.457310723 Simplifying x = 297.457310723Subproblem 2
x + -154 = -143.457310723 Simplifying x + -154 = -143.457310723 Reorder the terms: -154 + x = -143.457310723 Solving -154 + x = -143.457310723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '154' to each side of the equation. -154 + 154 + x = -143.457310723 + 154 Combine like terms: -154 + 154 = 0 0 + x = -143.457310723 + 154 x = -143.457310723 + 154 Combine like terms: -143.457310723 + 154 = 10.542689277 x = 10.542689277 Simplifying x = 10.542689277Solution
The solution to the problem is based on the solutions from the subproblems. x = {297.457310723, 10.542689277}
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