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Simplifying 5x2 + -4x + -20 = 2x + 2 Reorder the terms: -20 + -4x + 5x2 = 2x + 2 Reorder the terms: -20 + -4x + 5x2 = 2 + 2x Solving -20 + -4x + 5x2 = 2 + 2x Solving for variable 'x'. Reorder the terms: -20 + -2 + -4x + -2x + 5x2 = 2 + 2x + -2 + -2x Combine like terms: -20 + -2 = -22 -22 + -4x + -2x + 5x2 = 2 + 2x + -2 + -2x Combine like terms: -4x + -2x = -6x -22 + -6x + 5x2 = 2 + 2x + -2 + -2x Reorder the terms: -22 + -6x + 5x2 = 2 + -2 + 2x + -2x Combine like terms: 2 + -2 = 0 -22 + -6x + 5x2 = 0 + 2x + -2x -22 + -6x + 5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -22 + -6x + 5x2 = 0 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 = 2.781742423 x = 2.781742423 Simplifying x = 2.781742423Subproblem 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 = -1.581742423 x = -1.581742423 Simplifying x = -1.581742423Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.781742423, -1.581742423}
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