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Simplifying 5x2 + -22x + -10 = 0 Reorder the terms: -10 + -22x + 5x2 = 0 Solving -10 + -22x + 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'. -2 + -4.4x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -4.4x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -4.4x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4.4x + x2 = 0 + 2 -4.4x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4.4x + x2 = 2 The x term is -4.4x. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x + 4.84 + x2 = 2 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = 2 + 4.84 Combine like terms: 2 + 4.84 = 6.84 4.84 + -4.4x + x2 = 6.84 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 6.84 Calculate the square root of the right side: 2.615339366 Break this problem into two subproblems by setting (x + -2.2) equal to 2.615339366 and -2.615339366.Subproblem 1
x + -2.2 = 2.615339366 Simplifying x + -2.2 = 2.615339366 Reorder the terms: -2.2 + x = 2.615339366 Solving -2.2 + x = 2.615339366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 2.615339366 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 2.615339366 + 2.2 x = 2.615339366 + 2.2 Combine like terms: 2.615339366 + 2.2 = 4.815339366 x = 4.815339366 Simplifying x = 4.815339366Subproblem 2
x + -2.2 = -2.615339366 Simplifying x + -2.2 = -2.615339366 Reorder the terms: -2.2 + x = -2.615339366 Solving -2.2 + x = -2.615339366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -2.615339366 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -2.615339366 + 2.2 x = -2.615339366 + 2.2 Combine like terms: -2.615339366 + 2.2 = -0.415339366 x = -0.415339366 Simplifying x = -0.415339366Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.815339366, -0.415339366}
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