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Simplifying 0 = 16x2 + 90x + 6 Reorder the terms: 0 = 6 + 90x + 16x2 Solving 0 = 6 + 90x + 16x2 Solving for variable 'x'. Combine like terms: 0 + -6 = -6 -6 + -90x + -16x2 = 6 + 90x + 16x2 + -6 + -90x + -16x2 Reorder the terms: -6 + -90x + -16x2 = 6 + -6 + 90x + -90x + 16x2 + -16x2 Combine like terms: 6 + -6 = 0 -6 + -90x + -16x2 = 0 + 90x + -90x + 16x2 + -16x2 -6 + -90x + -16x2 = 90x + -90x + 16x2 + -16x2 Combine like terms: 90x + -90x = 0 -6 + -90x + -16x2 = 0 + 16x2 + -16x2 -6 + -90x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 -6 + -90x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(3 + 45x + 8x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3 + 45x + 8x2)' equal to zero and attempt to solve: Simplifying 3 + 45x + 8x2 = 0 Solving 3 + 45x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.375 + 5.625x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + 5.625x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + 5.625x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + 5.625x + x2 = 0 + -0.375 5.625x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 5.625x + x2 = -0.375 The x term is 5.625x. Take half its coefficient (2.8125). Square it (7.91015625) and add it to both sides. Add '7.91015625' to each side of the equation. 5.625x + 7.91015625 + x2 = -0.375 + 7.91015625 Reorder the terms: 7.91015625 + 5.625x + x2 = -0.375 + 7.91015625 Combine like terms: -0.375 + 7.91015625 = 7.53515625 7.91015625 + 5.625x + x2 = 7.53515625 Factor a perfect square on the left side: (x + 2.8125)(x + 2.8125) = 7.53515625 Calculate the square root of the right side: 2.745023907 Break this problem into two subproblems by setting (x + 2.8125) equal to 2.745023907 and -2.745023907.Subproblem 1
x + 2.8125 = 2.745023907 Simplifying x + 2.8125 = 2.745023907 Reorder the terms: 2.8125 + x = 2.745023907 Solving 2.8125 + x = 2.745023907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8125' to each side of the equation. 2.8125 + -2.8125 + x = 2.745023907 + -2.8125 Combine like terms: 2.8125 + -2.8125 = 0.0000 0.0000 + x = 2.745023907 + -2.8125 x = 2.745023907 + -2.8125 Combine like terms: 2.745023907 + -2.8125 = -0.067476093 x = -0.067476093 Simplifying x = -0.067476093Subproblem 2
x + 2.8125 = -2.745023907 Simplifying x + 2.8125 = -2.745023907 Reorder the terms: 2.8125 + x = -2.745023907 Solving 2.8125 + x = -2.745023907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8125' to each side of the equation. 2.8125 + -2.8125 + x = -2.745023907 + -2.8125 Combine like terms: 2.8125 + -2.8125 = 0.0000 0.0000 + x = -2.745023907 + -2.8125 x = -2.745023907 + -2.8125 Combine like terms: -2.745023907 + -2.8125 = -5.557523907 x = -5.557523907 Simplifying x = -5.557523907Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.067476093, -5.557523907}Solution
x = {-0.067476093, -5.557523907}
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