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Simplifying 16x2 + 15x + -35 = 0 Reorder the terms: -35 + 15x + 16x2 = 0 Solving -35 + 15x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.1875 + 0.9375x + x2 = 0 Move the constant term to the right: Add '2.1875' to each side of the equation. -2.1875 + 0.9375x + 2.1875 + x2 = 0 + 2.1875 Reorder the terms: -2.1875 + 2.1875 + 0.9375x + x2 = 0 + 2.1875 Combine like terms: -2.1875 + 2.1875 = 0.0000 0.0000 + 0.9375x + x2 = 0 + 2.1875 0.9375x + x2 = 0 + 2.1875 Combine like terms: 0 + 2.1875 = 2.1875 0.9375x + x2 = 2.1875 The x term is 0.9375x. Take half its coefficient (0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. 0.9375x + 0.2197265625 + x2 = 2.1875 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375x + x2 = 2.1875 + 0.2197265625 Combine like terms: 2.1875 + 0.2197265625 = 2.4072265625 0.2197265625 + 0.9375x + x2 = 2.4072265625 Factor a perfect square on the left side: (x + 0.46875)(x + 0.46875) = 2.4072265625 Calculate the square root of the right side: 1.551523948 Break this problem into two subproblems by setting (x + 0.46875) equal to 1.551523948 and -1.551523948.Subproblem 1
x + 0.46875 = 1.551523948 Simplifying x + 0.46875 = 1.551523948 Reorder the terms: 0.46875 + x = 1.551523948 Solving 0.46875 + x = 1.551523948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + x = 1.551523948 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + x = 1.551523948 + -0.46875 x = 1.551523948 + -0.46875 Combine like terms: 1.551523948 + -0.46875 = 1.082773948 x = 1.082773948 Simplifying x = 1.082773948Subproblem 2
x + 0.46875 = -1.551523948 Simplifying x + 0.46875 = -1.551523948 Reorder the terms: 0.46875 + x = -1.551523948 Solving 0.46875 + x = -1.551523948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + x = -1.551523948 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + x = -1.551523948 + -0.46875 x = -1.551523948 + -0.46875 Combine like terms: -1.551523948 + -0.46875 = -2.020273948 x = -2.020273948 Simplifying x = -2.020273948Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.082773948, -2.020273948}
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