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Simplifying 5x2 + -22x + -90 = 0 Reorder the terms: -90 + -22x + 5x2 = 0 Solving -90 + -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'. -18 + -4.4x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -4.4x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -4.4x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -4.4x + x2 = 0 + 18 -4.4x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -4.4x + x2 = 18 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 = 18 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = 18 + 4.84 Combine like terms: 18 + 4.84 = 22.84 4.84 + -4.4x + x2 = 22.84 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 22.84 Calculate the square root of the right side: 4.779121258 Break this problem into two subproblems by setting (x + -2.2) equal to 4.779121258 and -4.779121258.Subproblem 1
x + -2.2 = 4.779121258 Simplifying x + -2.2 = 4.779121258 Reorder the terms: -2.2 + x = 4.779121258 Solving -2.2 + x = 4.779121258 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 = 4.779121258 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 4.779121258 + 2.2 x = 4.779121258 + 2.2 Combine like terms: 4.779121258 + 2.2 = 6.979121258 x = 6.979121258 Simplifying x = 6.979121258Subproblem 2
x + -2.2 = -4.779121258 Simplifying x + -2.2 = -4.779121258 Reorder the terms: -2.2 + x = -4.779121258 Solving -2.2 + x = -4.779121258 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 = -4.779121258 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -4.779121258 + 2.2 x = -4.779121258 + 2.2 Combine like terms: -4.779121258 + 2.2 = -2.579121258 x = -2.579121258 Simplifying x = -2.579121258Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.979121258, -2.579121258}
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