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Simplifying 14x(8 + 7x) = 5 + -6x (8 * 14x + 7x * 14x) = 5 + -6x (112x + 98x2) = 5 + -6x Solving 112x + 98x2 = 5 + -6x Solving for variable 'x'. Reorder the terms: -5 + 112x + 6x + 98x2 = 5 + -6x + -5 + 6x Combine like terms: 112x + 6x = 118x -5 + 118x + 98x2 = 5 + -6x + -5 + 6x Reorder the terms: -5 + 118x + 98x2 = 5 + -5 + -6x + 6x Combine like terms: 5 + -5 = 0 -5 + 118x + 98x2 = 0 + -6x + 6x -5 + 118x + 98x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -5 + 118x + 98x2 = 0 Begin completing the square. Divide all terms by 98 the coefficient of the squared term: Divide each side by '98'. -0.05102040816 + 1.204081633x + x2 = 0 Move the constant term to the right: Add '0.05102040816' to each side of the equation. -0.05102040816 + 1.204081633x + 0.05102040816 + x2 = 0 + 0.05102040816 Reorder the terms: -0.05102040816 + 0.05102040816 + 1.204081633x + x2 = 0 + 0.05102040816 Combine like terms: -0.05102040816 + 0.05102040816 = 0.00000000000 0.00000000000 + 1.204081633x + x2 = 0 + 0.05102040816 1.204081633x + x2 = 0 + 0.05102040816 Combine like terms: 0 + 0.05102040816 = 0.05102040816 1.204081633x + x2 = 0.05102040816 The x term is 1.204081633x. Take half its coefficient (0.6020408165). Square it (0.3624531447) and add it to both sides. Add '0.3624531447' to each side of the equation. 1.204081633x + 0.3624531447 + x2 = 0.05102040816 + 0.3624531447 Reorder the terms: 0.3624531447 + 1.204081633x + x2 = 0.05102040816 + 0.3624531447 Combine like terms: 0.05102040816 + 0.3624531447 = 0.41347355286 0.3624531447 + 1.204081633x + x2 = 0.41347355286 Factor a perfect square on the left side: (x + 0.6020408165)(x + 0.6020408165) = 0.41347355286 Calculate the square root of the right side: 0.643019092 Break this problem into two subproblems by setting (x + 0.6020408165) equal to 0.643019092 and -0.643019092.Subproblem 1
x + 0.6020408165 = 0.643019092 Simplifying x + 0.6020408165 = 0.643019092 Reorder the terms: 0.6020408165 + x = 0.643019092 Solving 0.6020408165 + x = 0.643019092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6020408165' to each side of the equation. 0.6020408165 + -0.6020408165 + x = 0.643019092 + -0.6020408165 Combine like terms: 0.6020408165 + -0.6020408165 = 0.0000000000 0.0000000000 + x = 0.643019092 + -0.6020408165 x = 0.643019092 + -0.6020408165 Combine like terms: 0.643019092 + -0.6020408165 = 0.0409782755 x = 0.0409782755 Simplifying x = 0.0409782755Subproblem 2
x + 0.6020408165 = -0.643019092 Simplifying x + 0.6020408165 = -0.643019092 Reorder the terms: 0.6020408165 + x = -0.643019092 Solving 0.6020408165 + x = -0.643019092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6020408165' to each side of the equation. 0.6020408165 + -0.6020408165 + x = -0.643019092 + -0.6020408165 Combine like terms: 0.6020408165 + -0.6020408165 = 0.0000000000 0.0000000000 + x = -0.643019092 + -0.6020408165 x = -0.643019092 + -0.6020408165 Combine like terms: -0.643019092 + -0.6020408165 = -1.2450599085 x = -1.2450599085 Simplifying x = -1.2450599085Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0409782755, -1.2450599085}
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