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Simplifying 16x(9x + -20) = 8x + -25 Reorder the terms: 16x(-20 + 9x) = 8x + -25 (-20 * 16x + 9x * 16x) = 8x + -25 (-320x + 144x2) = 8x + -25 Reorder the terms: -320x + 144x2 = -25 + 8x Solving -320x + 144x2 = -25 + 8x Solving for variable 'x'. Reorder the terms: 25 + -320x + -8x + 144x2 = -25 + 8x + 25 + -8x Combine like terms: -320x + -8x = -328x 25 + -328x + 144x2 = -25 + 8x + 25 + -8x Reorder the terms: 25 + -328x + 144x2 = -25 + 25 + 8x + -8x Combine like terms: -25 + 25 = 0 25 + -328x + 144x2 = 0 + 8x + -8x 25 + -328x + 144x2 = 8x + -8x Combine like terms: 8x + -8x = 0 25 + -328x + 144x2 = 0 Begin completing the square. Divide all terms by 144 the coefficient of the squared term: Divide each side by '144'. 0.1736111111 + -2.277777778x + x2 = 0 Move the constant term to the right: Add '-0.1736111111' to each side of the equation. 0.1736111111 + -2.277777778x + -0.1736111111 + x2 = 0 + -0.1736111111 Reorder the terms: 0.1736111111 + -0.1736111111 + -2.277777778x + x2 = 0 + -0.1736111111 Combine like terms: 0.1736111111 + -0.1736111111 = 0.0000000000 0.0000000000 + -2.277777778x + x2 = 0 + -0.1736111111 -2.277777778x + x2 = 0 + -0.1736111111 Combine like terms: 0 + -0.1736111111 = -0.1736111111 -2.277777778x + x2 = -0.1736111111 The x term is -2.277777778x. Take half its coefficient (-1.138888889). Square it (1.297067901) and add it to both sides. Add '1.297067901' to each side of the equation. -2.277777778x + 1.297067901 + x2 = -0.1736111111 + 1.297067901 Reorder the terms: 1.297067901 + -2.277777778x + x2 = -0.1736111111 + 1.297067901 Combine like terms: -0.1736111111 + 1.297067901 = 1.1234567899 1.297067901 + -2.277777778x + x2 = 1.1234567899 Factor a perfect square on the left side: (x + -1.138888889)(x + -1.138888889) = 1.1234567899 Calculate the square root of the right side: 1.059932446 Break this problem into two subproblems by setting (x + -1.138888889) equal to 1.059932446 and -1.059932446.Subproblem 1
x + -1.138888889 = 1.059932446 Simplifying x + -1.138888889 = 1.059932446 Reorder the terms: -1.138888889 + x = 1.059932446 Solving -1.138888889 + x = 1.059932446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.138888889' to each side of the equation. -1.138888889 + 1.138888889 + x = 1.059932446 + 1.138888889 Combine like terms: -1.138888889 + 1.138888889 = 0.000000000 0.000000000 + x = 1.059932446 + 1.138888889 x = 1.059932446 + 1.138888889 Combine like terms: 1.059932446 + 1.138888889 = 2.198821335 x = 2.198821335 Simplifying x = 2.198821335Subproblem 2
x + -1.138888889 = -1.059932446 Simplifying x + -1.138888889 = -1.059932446 Reorder the terms: -1.138888889 + x = -1.059932446 Solving -1.138888889 + x = -1.059932446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.138888889' to each side of the equation. -1.138888889 + 1.138888889 + x = -1.059932446 + 1.138888889 Combine like terms: -1.138888889 + 1.138888889 = 0.000000000 0.000000000 + x = -1.059932446 + 1.138888889 x = -1.059932446 + 1.138888889 Combine like terms: -1.059932446 + 1.138888889 = 0.078956443 x = 0.078956443 Simplifying x = 0.078956443Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.198821335, 0.078956443}
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