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Simplifying 3.2x2 + 3x + -95 = 0 Reorder the terms: -95 + 3x + 3.2x2 = 0 Solving -95 + 3x + 3.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.2 the coefficient of the squared term: Divide each side by '3.2'. -29.6875 + 0.9375x + x2 = 0 Move the constant term to the right: Add '29.6875' to each side of the equation. -29.6875 + 0.9375x + 29.6875 + x2 = 0 + 29.6875 Reorder the terms: -29.6875 + 29.6875 + 0.9375x + x2 = 0 + 29.6875 Combine like terms: -29.6875 + 29.6875 = 0.0000 0.0000 + 0.9375x + x2 = 0 + 29.6875 0.9375x + x2 = 0 + 29.6875 Combine like terms: 0 + 29.6875 = 29.6875 0.9375x + x2 = 29.6875 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 = 29.6875 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375x + x2 = 29.6875 + 0.2197265625 Combine like terms: 29.6875 + 0.2197265625 = 29.9072265625 0.2197265625 + 0.9375x + x2 = 29.9072265625 Factor a perfect square on the left side: (x + 0.46875)(x + 0.46875) = 29.9072265625 Calculate the square root of the right side: 5.46875 Break this problem into two subproblems by setting (x + 0.46875) equal to 5.46875 and -5.46875.Subproblem 1
x + 0.46875 = 5.46875 Simplifying x + 0.46875 = 5.46875 Reorder the terms: 0.46875 + x = 5.46875 Solving 0.46875 + x = 5.46875 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 = 5.46875 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + x = 5.46875 + -0.46875 x = 5.46875 + -0.46875 Combine like terms: 5.46875 + -0.46875 = 5 x = 5 Simplifying x = 5Subproblem 2
x + 0.46875 = -5.46875 Simplifying x + 0.46875 = -5.46875 Reorder the terms: 0.46875 + x = -5.46875 Solving 0.46875 + x = -5.46875 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 = -5.46875 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + x = -5.46875 + -0.46875 x = -5.46875 + -0.46875 Combine like terms: -5.46875 + -0.46875 = -5.9375 x = -5.9375 Simplifying x = -5.9375Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, -5.9375}
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