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Simplifying 12x2 + 8x = 20 + 5x Reorder the terms: 8x + 12x2 = 20 + 5x Solving 8x + 12x2 = 20 + 5x Solving for variable 'x'. Reorder the terms: -20 + 8x + -5x + 12x2 = 20 + 5x + -20 + -5x Combine like terms: 8x + -5x = 3x -20 + 3x + 12x2 = 20 + 5x + -20 + -5x Reorder the terms: -20 + 3x + 12x2 = 20 + -20 + 5x + -5x Combine like terms: 20 + -20 = 0 -20 + 3x + 12x2 = 0 + 5x + -5x -20 + 3x + 12x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -20 + 3x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -1.666666667 + 0.25x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + 0.25x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + 0.25x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + 0.25x + x2 = 0 + 1.666666667 0.25x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 0.25x + x2 = 1.666666667 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 1.666666667 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 1.666666667 + 0.015625 Combine like terms: 1.666666667 + 0.015625 = 1.682291667 0.015625 + 0.25x + x2 = 1.682291667 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 1.682291667 Calculate the square root of the right side: 1.297031868 Break this problem into two subproblems by setting (x + 0.125) equal to 1.297031868 and -1.297031868.Subproblem 1
x + 0.125 = 1.297031868 Simplifying x + 0.125 = 1.297031868 Reorder the terms: 0.125 + x = 1.297031868 Solving 0.125 + x = 1.297031868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 1.297031868 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.297031868 + -0.125 x = 1.297031868 + -0.125 Combine like terms: 1.297031868 + -0.125 = 1.172031868 x = 1.172031868 Simplifying x = 1.172031868Subproblem 2
x + 0.125 = -1.297031868 Simplifying x + 0.125 = -1.297031868 Reorder the terms: 0.125 + x = -1.297031868 Solving 0.125 + x = -1.297031868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -1.297031868 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.297031868 + -0.125 x = -1.297031868 + -0.125 Combine like terms: -1.297031868 + -0.125 = -1.422031868 x = -1.422031868 Simplifying x = -1.422031868Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.172031868, -1.422031868}
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