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Simplifying 8.12x2 + 2.87x = 5.46 Reorder the terms: 2.87x + 8.12x2 = 5.46 Solving 2.87x + 8.12x2 = 5.46 Solving for variable 'x'. Reorder the terms: -5.46 + 2.87x + 8.12x2 = 5.46 + -5.46 Combine like terms: 5.46 + -5.46 = 0.00 -5.46 + 2.87x + 8.12x2 = 0.00 Begin completing the square. Divide all terms by 8.12 the coefficient of the squared term: Divide each side by '8.12'. -0.6724137931 + 0.3534482759x + x2 = 0 Move the constant term to the right: Add '0.6724137931' to each side of the equation. -0.6724137931 + 0.3534482759x + 0.6724137931 + x2 = 0 + 0.6724137931 Reorder the terms: -0.6724137931 + 0.6724137931 + 0.3534482759x + x2 = 0 + 0.6724137931 Combine like terms: -0.6724137931 + 0.6724137931 = 0.0000000000 0.0000000000 + 0.3534482759x + x2 = 0 + 0.6724137931 0.3534482759x + x2 = 0 + 0.6724137931 Combine like terms: 0 + 0.6724137931 = 0.6724137931 0.3534482759x + x2 = 0.6724137931 The x term is 0.3534482759x. Take half its coefficient (0.176724138). Square it (0.03123142095) and add it to both sides. Add '0.03123142095' to each side of the equation. 0.3534482759x + 0.03123142095 + x2 = 0.6724137931 + 0.03123142095 Reorder the terms: 0.03123142095 + 0.3534482759x + x2 = 0.6724137931 + 0.03123142095 Combine like terms: 0.6724137931 + 0.03123142095 = 0.70364521405 0.03123142095 + 0.3534482759x + x2 = 0.70364521405 Factor a perfect square on the left side: (x + 0.176724138)(x + 0.176724138) = 0.70364521405 Calculate the square root of the right side: 0.83883563 Break this problem into two subproblems by setting (x + 0.176724138) equal to 0.83883563 and -0.83883563.Subproblem 1
x + 0.176724138 = 0.83883563 Simplifying x + 0.176724138 = 0.83883563 Reorder the terms: 0.176724138 + x = 0.83883563 Solving 0.176724138 + x = 0.83883563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.176724138' to each side of the equation. 0.176724138 + -0.176724138 + x = 0.83883563 + -0.176724138 Combine like terms: 0.176724138 + -0.176724138 = 0.000000000 0.000000000 + x = 0.83883563 + -0.176724138 x = 0.83883563 + -0.176724138 Combine like terms: 0.83883563 + -0.176724138 = 0.662111492 x = 0.662111492 Simplifying x = 0.662111492Subproblem 2
x + 0.176724138 = -0.83883563 Simplifying x + 0.176724138 = -0.83883563 Reorder the terms: 0.176724138 + x = -0.83883563 Solving 0.176724138 + x = -0.83883563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.176724138' to each side of the equation. 0.176724138 + -0.176724138 + x = -0.83883563 + -0.176724138 Combine like terms: 0.176724138 + -0.176724138 = 0.000000000 0.000000000 + x = -0.83883563 + -0.176724138 x = -0.83883563 + -0.176724138 Combine like terms: -0.83883563 + -0.176724138 = -1.015559768 x = -1.015559768 Simplifying x = -1.015559768Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.662111492, -1.015559768}
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