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Simplifying 5x2 + 21x + -22 = 0 Reorder the terms: -22 + 21x + 5x2 = 0 Solving -22 + 21x + 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'. -4.4 + 4.2x + x2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + 4.2x + 4.4 + x2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + 4.2x + x2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + 4.2x + x2 = 0 + 4.4 4.2x + x2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 4.2x + x2 = 4.4 The x term is 4.2x. Take half its coefficient (2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. 4.2x + 4.41 + x2 = 4.4 + 4.41 Reorder the terms: 4.41 + 4.2x + x2 = 4.4 + 4.41 Combine like terms: 4.4 + 4.41 = 8.81 4.41 + 4.2x + x2 = 8.81 Factor a perfect square on the left side: (x + 2.1)(x + 2.1) = 8.81 Calculate the square root of the right side: 2.968164416 Break this problem into two subproblems by setting (x + 2.1) equal to 2.968164416 and -2.968164416.Subproblem 1
x + 2.1 = 2.968164416 Simplifying x + 2.1 = 2.968164416 Reorder the terms: 2.1 + x = 2.968164416 Solving 2.1 + x = 2.968164416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = 2.968164416 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = 2.968164416 + -2.1 x = 2.968164416 + -2.1 Combine like terms: 2.968164416 + -2.1 = 0.868164416 x = 0.868164416 Simplifying x = 0.868164416Subproblem 2
x + 2.1 = -2.968164416 Simplifying x + 2.1 = -2.968164416 Reorder the terms: 2.1 + x = -2.968164416 Solving 2.1 + x = -2.968164416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.1' to each side of the equation. 2.1 + -2.1 + x = -2.968164416 + -2.1 Combine like terms: 2.1 + -2.1 = 0.0 0.0 + x = -2.968164416 + -2.1 x = -2.968164416 + -2.1 Combine like terms: -2.968164416 + -2.1 = -5.068164416 x = -5.068164416 Simplifying x = -5.068164416Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.868164416, -5.068164416}
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