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Simplifying 12 + 2x = 5x2 + -8 Reorder the terms: 12 + 2x = -8 + 5x2 Solving 12 + 2x = -8 + 5x2 Solving for variable 'x'. Reorder the terms: 12 + 8 + 2x + -5x2 = -8 + 5x2 + 8 + -5x2 Combine like terms: 12 + 8 = 20 20 + 2x + -5x2 = -8 + 5x2 + 8 + -5x2 Reorder the terms: 20 + 2x + -5x2 = -8 + 8 + 5x2 + -5x2 Combine like terms: -8 + 8 = 0 20 + 2x + -5x2 = 0 + 5x2 + -5x2 20 + 2x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 20 + 2x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -4 + -0.4x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -0.4x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -0.4x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -0.4x + x2 = 0 + 4 -0.4x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -0.4x + x2 = 4 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 4 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 4 + 0.04 Combine like terms: 4 + 0.04 = 4.04 0.04 + -0.4x + x2 = 4.04 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 4.04 Calculate the square root of the right side: 2.009975124 Break this problem into two subproblems by setting (x + -0.2) equal to 2.009975124 and -2.009975124.Subproblem 1
x + -0.2 = 2.009975124 Simplifying x + -0.2 = 2.009975124 Reorder the terms: -0.2 + x = 2.009975124 Solving -0.2 + x = 2.009975124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 2.009975124 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 2.009975124 + 0.2 x = 2.009975124 + 0.2 Combine like terms: 2.009975124 + 0.2 = 2.209975124 x = 2.209975124 Simplifying x = 2.209975124Subproblem 2
x + -0.2 = -2.009975124 Simplifying x + -0.2 = -2.009975124 Reorder the terms: -0.2 + x = -2.009975124 Solving -0.2 + x = -2.009975124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -2.009975124 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -2.009975124 + 0.2 x = -2.009975124 + 0.2 Combine like terms: -2.009975124 + 0.2 = -1.809975124 x = -1.809975124 Simplifying x = -1.809975124Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.209975124, -1.809975124}
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