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Simplifying (9x + -4)(9x + -4) = 17 Reorder the terms: (-4 + 9x)(9x + -4) = 17 Reorder the terms: (-4 + 9x)(-4 + 9x) = 17 Multiply (-4 + 9x) * (-4 + 9x) (-4(-4 + 9x) + 9x * (-4 + 9x)) = 17 ((-4 * -4 + 9x * -4) + 9x * (-4 + 9x)) = 17 ((16 + -36x) + 9x * (-4 + 9x)) = 17 (16 + -36x + (-4 * 9x + 9x * 9x)) = 17 (16 + -36x + (-36x + 81x2)) = 17 Combine like terms: -36x + -36x = -72x (16 + -72x + 81x2) = 17 Solving 16 + -72x + 81x2 = 17 Solving for variable 'x'. Reorder the terms: 16 + -17 + -72x + 81x2 = 17 + -17 Combine like terms: 16 + -17 = -1 -1 + -72x + 81x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -1 + -72x + 81x2 = 0 Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. -0.01234567901 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '0.01234567901' to each side of the equation. -0.01234567901 + -0.8888888889x + 0.01234567901 + x2 = 0 + 0.01234567901 Reorder the terms: -0.01234567901 + 0.01234567901 + -0.8888888889x + x2 = 0 + 0.01234567901 Combine like terms: -0.01234567901 + 0.01234567901 = 0.00000000000 0.00000000000 + -0.8888888889x + x2 = 0 + 0.01234567901 -0.8888888889x + x2 = 0 + 0.01234567901 Combine like terms: 0 + 0.01234567901 = 0.01234567901 -0.8888888889x + x2 = 0.01234567901 The x term is -0.8888888889x. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889x + 0.1975308642 + x2 = 0.01234567901 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 0.01234567901 + 0.1975308642 Combine like terms: 0.01234567901 + 0.1975308642 = 0.20987654321 0.1975308642 + -0.8888888889x + x2 = 0.20987654321 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 0.20987654321 Calculate the square root of the right side: 0.458122847 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 0.458122847 and -0.458122847.Subproblem 1
x + -0.4444444445 = 0.458122847 Simplifying x + -0.4444444445 = 0.458122847 Reorder the terms: -0.4444444445 + x = 0.458122847 Solving -0.4444444445 + x = 0.458122847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 0.458122847 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 0.458122847 + 0.4444444445 x = 0.458122847 + 0.4444444445 Combine like terms: 0.458122847 + 0.4444444445 = 0.9025672915 x = 0.9025672915 Simplifying x = 0.9025672915Subproblem 2
x + -0.4444444445 = -0.458122847 Simplifying x + -0.4444444445 = -0.458122847 Reorder the terms: -0.4444444445 + x = -0.458122847 Solving -0.4444444445 + x = -0.458122847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -0.458122847 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -0.458122847 + 0.4444444445 x = -0.458122847 + 0.4444444445 Combine like terms: -0.458122847 + 0.4444444445 = -0.0136784025 x = -0.0136784025 Simplifying x = -0.0136784025Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9025672915, -0.0136784025}
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