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Simplifying 5x2 + 6x + -22 = 0 Reorder the terms: -22 + 6x + 5x2 = 0 Solving -22 + 6x + 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 + 1.2x + x2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + 1.2x + 4.4 + x2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + 1.2x + x2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + 1.2x + x2 = 0 + 4.4 1.2x + x2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 1.2x + x2 = 4.4 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 4.4 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 4.4 + 0.36 Combine like terms: 4.4 + 0.36 = 4.76 0.36 + 1.2x + x2 = 4.76 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 4.76 Calculate the square root of the right side: 2.181742423 Break this problem into two subproblems by setting (x + 0.6) equal to 2.181742423 and -2.181742423.Subproblem 1
x + 0.6 = 2.181742423 Simplifying x + 0.6 = 2.181742423 Reorder the terms: 0.6 + x = 2.181742423 Solving 0.6 + x = 2.181742423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 2.181742423 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 2.181742423 + -0.6 x = 2.181742423 + -0.6 Combine like terms: 2.181742423 + -0.6 = 1.581742423 x = 1.581742423 Simplifying x = 1.581742423Subproblem 2
x + 0.6 = -2.181742423 Simplifying x + 0.6 = -2.181742423 Reorder the terms: 0.6 + x = -2.181742423 Solving 0.6 + x = -2.181742423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -2.181742423 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -2.181742423 + -0.6 x = -2.181742423 + -0.6 Combine like terms: -2.181742423 + -0.6 = -2.781742423 x = -2.781742423 Simplifying x = -2.781742423Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.581742423, -2.781742423}
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