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Simplifying 5x2 + -10x + -246 = 0 Reorder the terms: -246 + -10x + 5x2 = 0 Solving -246 + -10x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -49.2 + -2x + x2 = 0 Move the constant term to the right: Add '49.2' to each side of the equation. -49.2 + -2x + 49.2 + x2 = 0 + 49.2 Reorder the terms: -49.2 + 49.2 + -2x + x2 = 0 + 49.2 Combine like terms: -49.2 + 49.2 = 0.0 0.0 + -2x + x2 = 0 + 49.2 -2x + x2 = 0 + 49.2 Combine like terms: 0 + 49.2 = 49.2 -2x + x2 = 49.2 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 49.2 + 1 Reorder the terms: 1 + -2x + x2 = 49.2 + 1 Combine like terms: 49.2 + 1 = 50.2 1 + -2x + x2 = 50.2 Factor a perfect square on the left side: (x + -1)(x + -1) = 50.2 Calculate the square root of the right side: 7.085195834 Break this problem into two subproblems by setting (x + -1) equal to 7.085195834 and -7.085195834.Subproblem 1
x + -1 = 7.085195834 Simplifying x + -1 = 7.085195834 Reorder the terms: -1 + x = 7.085195834 Solving -1 + x = 7.085195834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 7.085195834 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.085195834 + 1 x = 7.085195834 + 1 Combine like terms: 7.085195834 + 1 = 8.085195834 x = 8.085195834 Simplifying x = 8.085195834Subproblem 2
x + -1 = -7.085195834 Simplifying x + -1 = -7.085195834 Reorder the terms: -1 + x = -7.085195834 Solving -1 + x = -7.085195834 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -7.085195834 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.085195834 + 1 x = -7.085195834 + 1 Combine like terms: -7.085195834 + 1 = -6.085195834 x = -6.085195834 Simplifying x = -6.085195834Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.085195834, -6.085195834}
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