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Simplifying 81x2 + -225x + -625 = 0 Reorder the terms: -625 + -225x + 81x2 = 0 Solving -625 + -225x + 81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -7.716049383 + -2.777777778x + x2 = 0 Move the constant term to the right: Add '7.716049383' to each side of the equation. -7.716049383 + -2.777777778x + 7.716049383 + x2 = 0 + 7.716049383 Reorder the terms: -7.716049383 + 7.716049383 + -2.777777778x + x2 = 0 + 7.716049383 Combine like terms: -7.716049383 + 7.716049383 = 0.000000000 0.000000000 + -2.777777778x + x2 = 0 + 7.716049383 -2.777777778x + x2 = 0 + 7.716049383 Combine like terms: 0 + 7.716049383 = 7.716049383 -2.777777778x + x2 = 7.716049383 The x term is -2.777777778x. Take half its coefficient (-1.388888889). Square it (1.929012346) and add it to both sides. Add '1.929012346' to each side of the equation. -2.777777778x + 1.929012346 + x2 = 7.716049383 + 1.929012346 Reorder the terms: 1.929012346 + -2.777777778x + x2 = 7.716049383 + 1.929012346 Combine like terms: 7.716049383 + 1.929012346 = 9.645061729 1.929012346 + -2.777777778x + x2 = 9.645061729 Factor a perfect square on the left side: (x + -1.388888889)(x + -1.388888889) = 9.645061729 Calculate the square root of the right side: 3.105649969 Break this problem into two subproblems by setting (x + -1.388888889) equal to 3.105649969 and -3.105649969.Subproblem 1
x + -1.388888889 = 3.105649969 Simplifying x + -1.388888889 = 3.105649969 Reorder the terms: -1.388888889 + x = 3.105649969 Solving -1.388888889 + x = 3.105649969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x = 3.105649969 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = 3.105649969 + 1.388888889 x = 3.105649969 + 1.388888889 Combine like terms: 3.105649969 + 1.388888889 = 4.494538858 x = 4.494538858 Simplifying x = 4.494538858Subproblem 2
x + -1.388888889 = -3.105649969 Simplifying x + -1.388888889 = -3.105649969 Reorder the terms: -1.388888889 + x = -3.105649969 Solving -1.388888889 + x = -3.105649969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.388888889' to each side of the equation. -1.388888889 + 1.388888889 + x = -3.105649969 + 1.388888889 Combine like terms: -1.388888889 + 1.388888889 = 0.000000000 0.000000000 + x = -3.105649969 + 1.388888889 x = -3.105649969 + 1.388888889 Combine like terms: -3.105649969 + 1.388888889 = -1.71676108 x = -1.71676108 Simplifying x = -1.71676108Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.494538858, -1.71676108}
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