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Simplifying -1x2 + 4x + 490 = 0 Reorder the terms: 490 + 4x + -1x2 = 0 Solving 490 + 4x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -490 + -4x + x2 = 0 Move the constant term to the right: Add '490' to each side of the equation. -490 + -4x + 490 + x2 = 0 + 490 Reorder the terms: -490 + 490 + -4x + x2 = 0 + 490 Combine like terms: -490 + 490 = 0 0 + -4x + x2 = 0 + 490 -4x + x2 = 0 + 490 Combine like terms: 0 + 490 = 490 -4x + x2 = 490 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 490 + 4 Reorder the terms: 4 + -4x + x2 = 490 + 4 Combine like terms: 490 + 4 = 494 4 + -4x + x2 = 494 Factor a perfect square on the left side: (x + -2)(x + -2) = 494 Calculate the square root of the right side: 22.226110771 Break this problem into two subproblems by setting (x + -2) equal to 22.226110771 and -22.226110771.Subproblem 1
x + -2 = 22.226110771 Simplifying x + -2 = 22.226110771 Reorder the terms: -2 + x = 22.226110771 Solving -2 + x = 22.226110771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 22.226110771 + 2 Combine like terms: -2 + 2 = 0 0 + x = 22.226110771 + 2 x = 22.226110771 + 2 Combine like terms: 22.226110771 + 2 = 24.226110771 x = 24.226110771 Simplifying x = 24.226110771Subproblem 2
x + -2 = -22.226110771 Simplifying x + -2 = -22.226110771 Reorder the terms: -2 + x = -22.226110771 Solving -2 + x = -22.226110771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -22.226110771 + 2 Combine like terms: -2 + 2 = 0 0 + x = -22.226110771 + 2 x = -22.226110771 + 2 Combine like terms: -22.226110771 + 2 = -20.226110771 x = -20.226110771 Simplifying x = -20.226110771Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.226110771, -20.226110771}
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