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Simplifying (27x2) + (139x) + 707 = 1300 Reorder the terms: 707 + (139x) + (27x2) = 1300 Solving 707 + (139x) + (27x2) = 1300 Solving for variable 'x'. Reorder the terms: 707 + -1300 + (139x) + (27x2) = 1300 + -1300 Combine like terms: 707 + -1300 = -593 -593 + (139x) + (27x2) = 1300 + -1300 Combine like terms: 1300 + -1300 = 0 -593 + (139x) + (27x2) = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -21.96296296 + (5.148148148x) + x2 = 0 Move the constant term to the right: Add '21.96296296' to each side of the equation. -21.96296296 + (5.148148148x) + 21.96296296 + x2 = 0 + 21.96296296 Reorder the terms: -21.96296296 + 21.96296296 + (5.148148148x) + x2 = 0 + 21.96296296 Combine like terms: -21.96296296 + 21.96296296 = 0.00000000 0.00000000 + (5.148148148x) + x2 = 0 + 21.96296296 (5.148148148x) + x2 = 0 + 21.96296296 Combine like terms: 0 + 21.96296296 = 21.96296296 (5.148148148x) + x2 = 21.96296296 The x term is (5.148148148x). Take half its coefficient (2.574074074). Square it (6.625857338) and add it to both sides. Add '6.625857338' to each side of the equation. (5.148148148x) + 6.625857338 + x2 = 21.96296296 + 6.625857338 Reorder the terms: 6.625857338 + (5.148148148x) + x2 = 21.96296296 + 6.625857338 Combine like terms: 21.96296296 + 6.625857338 = 28.588820298 6.625857338 + (5.148148148x) + x2 = 28.588820298 Factor a perfect square on the left side: ((x) + 2.574074074)((x) + 2.574074074) = 28.588820298 Calculate the square root of the right side: 5.346851438 Break this problem into two subproblems by setting ((x) + 2.574074074) equal to 5.346851438 and -5.346851438.Subproblem 1
(x) + 2.574074074 = 5.346851438 Simplifying (x) + 2.574074074 = 5.346851438 x + 2.574074074 = 5.346851438 Reorder the terms: 2.574074074 + x = 5.346851438 Solving 2.574074074 + x = 5.346851438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.574074074' to each side of the equation. 2.574074074 + -2.574074074 + x = 5.346851438 + -2.574074074 Combine like terms: 2.574074074 + -2.574074074 = 0.000000000 0.000000000 + x = 5.346851438 + -2.574074074 x = 5.346851438 + -2.574074074 Combine like terms: 5.346851438 + -2.574074074 = 2.772777364 x = 2.772777364 Simplifying x = 2.772777364Subproblem 2
(x) + 2.574074074 = -5.346851438 Simplifying (x) + 2.574074074 = -5.346851438 x + 2.574074074 = -5.346851438 Reorder the terms: 2.574074074 + x = -5.346851438 Solving 2.574074074 + x = -5.346851438 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.574074074' to each side of the equation. 2.574074074 + -2.574074074 + x = -5.346851438 + -2.574074074 Combine like terms: 2.574074074 + -2.574074074 = 0.000000000 0.000000000 + x = -5.346851438 + -2.574074074 x = -5.346851438 + -2.574074074 Combine like terms: -5.346851438 + -2.574074074 = -7.920925512 x = -7.920925512 Simplifying x = -7.920925512Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.772777364, -7.920925512}
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