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Simplifying 2x2 + 5 + 20x = 20 + -8x2 + 8 Reorder the terms: 5 + 20x + 2x2 = 20 + -8x2 + 8 Reorder the terms: 5 + 20x + 2x2 = 20 + 8 + -8x2 Combine like terms: 20 + 8 = 28 5 + 20x + 2x2 = 28 + -8x2 Solving 5 + 20x + 2x2 = 28 + -8x2 Solving for variable 'x'. Reorder the terms: 5 + -28 + 20x + 2x2 + 8x2 = 28 + -8x2 + -28 + 8x2 Combine like terms: 5 + -28 = -23 -23 + 20x + 2x2 + 8x2 = 28 + -8x2 + -28 + 8x2 Combine like terms: 2x2 + 8x2 = 10x2 -23 + 20x + 10x2 = 28 + -8x2 + -28 + 8x2 Reorder the terms: -23 + 20x + 10x2 = 28 + -28 + -8x2 + 8x2 Combine like terms: 28 + -28 = 0 -23 + 20x + 10x2 = 0 + -8x2 + 8x2 -23 + 20x + 10x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 -23 + 20x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.3 + 2x + x2 = 0.0 Move the constant term to the right: Add '2.3' to each side of the equation. -2.3 + 2x + 2.3 + x2 = 0.0 + 2.3 Reorder the terms: -2.3 + 2.3 + 2x + x2 = 0.0 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + 2x + x2 = 0.0 + 2.3 2x + x2 = 0.0 + 2.3 Combine like terms: 0.0 + 2.3 = 2.3 2x + x2 = 2.3 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 2.3 + 1 Reorder the terms: 1 + 2x + x2 = 2.3 + 1 Combine like terms: 2.3 + 1 = 3.3 1 + 2x + x2 = 3.3 Factor a perfect square on the left side: (x + 1)(x + 1) = 3.3 Calculate the square root of the right side: 1.816590212 Break this problem into two subproblems by setting (x + 1) equal to 1.816590212 and -1.816590212.Subproblem 1
x + 1 = 1.816590212 Simplifying x + 1 = 1.816590212 Reorder the terms: 1 + x = 1.816590212 Solving 1 + x = 1.816590212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.816590212 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.816590212 + -1 x = 1.816590212 + -1 Combine like terms: 1.816590212 + -1 = 0.816590212 x = 0.816590212 Simplifying x = 0.816590212Subproblem 2
x + 1 = -1.816590212 Simplifying x + 1 = -1.816590212 Reorder the terms: 1 + x = -1.816590212 Solving 1 + x = -1.816590212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.816590212 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.816590212 + -1 x = -1.816590212 + -1 Combine like terms: -1.816590212 + -1 = -2.816590212 x = -2.816590212 Simplifying x = -2.816590212Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.816590212, -2.816590212}
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