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Simplifying 9x * x + 7x + 2 = 180 Multiply x * x 9x2 + 7x + 2 = 180 Reorder the terms: 2 + 7x + 9x2 = 180 Solving 2 + 7x + 9x2 = 180 Solving for variable 'x'. Reorder the terms: 2 + -180 + 7x + 9x2 = 180 + -180 Combine like terms: 2 + -180 = -178 -178 + 7x + 9x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -178 + 7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -19.77777778 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '19.77777778' to each side of the equation. -19.77777778 + 0.7777777778x + 19.77777778 + x2 = 0 + 19.77777778 Reorder the terms: -19.77777778 + 19.77777778 + 0.7777777778x + x2 = 0 + 19.77777778 Combine like terms: -19.77777778 + 19.77777778 = 0.00000000 0.00000000 + 0.7777777778x + x2 = 0 + 19.77777778 0.7777777778x + x2 = 0 + 19.77777778 Combine like terms: 0 + 19.77777778 = 19.77777778 0.7777777778x + x2 = 19.77777778 The x term is 0.7777777778x. Take half its coefficient (0.3888888889). Square it (0.1512345679) and add it to both sides. Add '0.1512345679' to each side of the equation. 0.7777777778x + 0.1512345679 + x2 = 19.77777778 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = 19.77777778 + 0.1512345679 Combine like terms: 19.77777778 + 0.1512345679 = 19.9290123479 0.1512345679 + 0.7777777778x + x2 = 19.9290123479 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 19.9290123479 Calculate the square root of the right side: 4.464192239 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 4.464192239 and -4.464192239.Subproblem 1
x + 0.3888888889 = 4.464192239 Simplifying x + 0.3888888889 = 4.464192239 Reorder the terms: 0.3888888889 + x = 4.464192239 Solving 0.3888888889 + x = 4.464192239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = 4.464192239 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 4.464192239 + -0.3888888889 x = 4.464192239 + -0.3888888889 Combine like terms: 4.464192239 + -0.3888888889 = 4.0753033501 x = 4.0753033501 Simplifying x = 4.0753033501Subproblem 2
x + 0.3888888889 = -4.464192239 Simplifying x + 0.3888888889 = -4.464192239 Reorder the terms: 0.3888888889 + x = -4.464192239 Solving 0.3888888889 + x = -4.464192239 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3888888889' to each side of the equation. 0.3888888889 + -0.3888888889 + x = -4.464192239 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -4.464192239 + -0.3888888889 x = -4.464192239 + -0.3888888889 Combine like terms: -4.464192239 + -0.3888888889 = -4.8530811279 x = -4.8530811279 Simplifying x = -4.8530811279Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.0753033501, -4.8530811279}
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