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Simplifying 6x(124 + x) = 797 (124 * 6x + x * 6x) = 797 (744x + 6x2) = 797 Solving 744x + 6x2 = 797 Solving for variable 'x'. Reorder the terms: -797 + 744x + 6x2 = 797 + -797 Combine like terms: 797 + -797 = 0 -797 + 744x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -132.8333333 + 124x + x2 = 0 Move the constant term to the right: Add '132.8333333' to each side of the equation. -132.8333333 + 124x + 132.8333333 + x2 = 0 + 132.8333333 Reorder the terms: -132.8333333 + 132.8333333 + 124x + x2 = 0 + 132.8333333 Combine like terms: -132.8333333 + 132.8333333 = 0.0000000 0.0000000 + 124x + x2 = 0 + 132.8333333 124x + x2 = 0 + 132.8333333 Combine like terms: 0 + 132.8333333 = 132.8333333 124x + x2 = 132.8333333 The x term is 124x. Take half its coefficient (62). Square it (3844) and add it to both sides. Add '3844' to each side of the equation. 124x + 3844 + x2 = 132.8333333 + 3844 Reorder the terms: 3844 + 124x + x2 = 132.8333333 + 3844 Combine like terms: 132.8333333 + 3844 = 3976.8333333 3844 + 124x + x2 = 3976.8333333 Factor a perfect square on the left side: (x + 62)(x + 62) = 3976.8333333 Calculate the square root of the right side: 63.062138667 Break this problem into two subproblems by setting (x + 62) equal to 63.062138667 and -63.062138667.Subproblem 1
x + 62 = 63.062138667 Simplifying x + 62 = 63.062138667 Reorder the terms: 62 + x = 63.062138667 Solving 62 + x = 63.062138667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62' to each side of the equation. 62 + -62 + x = 63.062138667 + -62 Combine like terms: 62 + -62 = 0 0 + x = 63.062138667 + -62 x = 63.062138667 + -62 Combine like terms: 63.062138667 + -62 = 1.062138667 x = 1.062138667 Simplifying x = 1.062138667Subproblem 2
x + 62 = -63.062138667 Simplifying x + 62 = -63.062138667 Reorder the terms: 62 + x = -63.062138667 Solving 62 + x = -63.062138667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-62' to each side of the equation. 62 + -62 + x = -63.062138667 + -62 Combine like terms: 62 + -62 = 0 0 + x = -63.062138667 + -62 x = -63.062138667 + -62 Combine like terms: -63.062138667 + -62 = -125.062138667 x = -125.062138667 Simplifying x = -125.062138667Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.062138667, -125.062138667}
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