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Simplifying -9x2 + 3 + -7x = 4 Reorder the terms: 3 + -7x + -9x2 = 4 Solving 3 + -7x + -9x2 = 4 Solving for variable 'x'. Reorder the terms: 3 + -4 + -7x + -9x2 = 4 + -4 Combine like terms: 3 + -4 = -1 -1 + -7x + -9x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -1 + -7x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(1 + 7x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(1 + 7x + 9x2)' equal to zero and attempt to solve: Simplifying 1 + 7x + 9x2 = 0 Solving 1 + 7x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.1111111111 + 0.7777777778x + x2 = 0 Move the constant term to the right: Add '-0.1111111111' to each side of the equation. 0.1111111111 + 0.7777777778x + -0.1111111111 + x2 = 0 + -0.1111111111 Reorder the terms: 0.1111111111 + -0.1111111111 + 0.7777777778x + x2 = 0 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + 0.7777777778x + x2 = 0 + -0.1111111111 0.7777777778x + x2 = 0 + -0.1111111111 Combine like terms: 0 + -0.1111111111 = -0.1111111111 0.7777777778x + x2 = -0.1111111111 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 = -0.1111111111 + 0.1512345679 Reorder the terms: 0.1512345679 + 0.7777777778x + x2 = -0.1111111111 + 0.1512345679 Combine like terms: -0.1111111111 + 0.1512345679 = 0.0401234568 0.1512345679 + 0.7777777778x + x2 = 0.0401234568 Factor a perfect square on the left side: (x + 0.3888888889)(x + 0.3888888889) = 0.0401234568 Calculate the square root of the right side: 0.200308404 Break this problem into two subproblems by setting (x + 0.3888888889) equal to 0.200308404 and -0.200308404.Subproblem 1
x + 0.3888888889 = 0.200308404 Simplifying x + 0.3888888889 = 0.200308404 Reorder the terms: 0.3888888889 + x = 0.200308404 Solving 0.3888888889 + x = 0.200308404 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 = 0.200308404 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = 0.200308404 + -0.3888888889 x = 0.200308404 + -0.3888888889 Combine like terms: 0.200308404 + -0.3888888889 = -0.1885804849 x = -0.1885804849 Simplifying x = -0.1885804849Subproblem 2
x + 0.3888888889 = -0.200308404 Simplifying x + 0.3888888889 = -0.200308404 Reorder the terms: 0.3888888889 + x = -0.200308404 Solving 0.3888888889 + x = -0.200308404 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 = -0.200308404 + -0.3888888889 Combine like terms: 0.3888888889 + -0.3888888889 = 0.0000000000 0.0000000000 + x = -0.200308404 + -0.3888888889 x = -0.200308404 + -0.3888888889 Combine like terms: -0.200308404 + -0.3888888889 = -0.5891972929 x = -0.5891972929 Simplifying x = -0.5891972929Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1885804849, -0.5891972929}Solution
x = {-0.1885804849, -0.5891972929}
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