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Simplifying 5x2 + 22x + -30 = 0 Reorder the terms: -30 + 22x + 5x2 = 0 Solving -30 + 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'. -6 + 4.4x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 4.4x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 4.4x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 4.4x + x2 = 0 + 6 4.4x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 4.4x + x2 = 6 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 = 6 + 4.84 Reorder the terms: 4.84 + 4.4x + x2 = 6 + 4.84 Combine like terms: 6 + 4.84 = 10.84 4.84 + 4.4x + x2 = 10.84 Factor a perfect square on the left side: (x + 2.2)(x + 2.2) = 10.84 Calculate the square root of the right side: 3.292415527 Break this problem into two subproblems by setting (x + 2.2) equal to 3.292415527 and -3.292415527.Subproblem 1
x + 2.2 = 3.292415527 Simplifying x + 2.2 = 3.292415527 Reorder the terms: 2.2 + x = 3.292415527 Solving 2.2 + x = 3.292415527 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 = 3.292415527 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = 3.292415527 + -2.2 x = 3.292415527 + -2.2 Combine like terms: 3.292415527 + -2.2 = 1.092415527 x = 1.092415527 Simplifying x = 1.092415527Subproblem 2
x + 2.2 = -3.292415527 Simplifying x + 2.2 = -3.292415527 Reorder the terms: 2.2 + x = -3.292415527 Solving 2.2 + x = -3.292415527 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 = -3.292415527 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = -3.292415527 + -2.2 x = -3.292415527 + -2.2 Combine like terms: -3.292415527 + -2.2 = -5.492415527 x = -5.492415527 Simplifying x = -5.492415527Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.092415527, -5.492415527}
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