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Simplifying 32x2 + -54x + -5 = 0 Reorder the terms: -5 + -54x + 32x2 = 0 Solving -5 + -54x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.15625 + -1.6875x + x2 = 0 Move the constant term to the right: Add '0.15625' to each side of the equation. -0.15625 + -1.6875x + 0.15625 + x2 = 0 + 0.15625 Reorder the terms: -0.15625 + 0.15625 + -1.6875x + x2 = 0 + 0.15625 Combine like terms: -0.15625 + 0.15625 = 0.00000 0.00000 + -1.6875x + x2 = 0 + 0.15625 -1.6875x + x2 = 0 + 0.15625 Combine like terms: 0 + 0.15625 = 0.15625 -1.6875x + x2 = 0.15625 The x term is -1.6875x. Take half its coefficient (-0.84375). Square it (0.7119140625) and add it to both sides. Add '0.7119140625' to each side of the equation. -1.6875x + 0.7119140625 + x2 = 0.15625 + 0.7119140625 Reorder the terms: 0.7119140625 + -1.6875x + x2 = 0.15625 + 0.7119140625 Combine like terms: 0.15625 + 0.7119140625 = 0.8681640625 0.7119140625 + -1.6875x + x2 = 0.8681640625 Factor a perfect square on the left side: (x + -0.84375)(x + -0.84375) = 0.8681640625 Calculate the square root of the right side: 0.93175322 Break this problem into two subproblems by setting (x + -0.84375) equal to 0.93175322 and -0.93175322.Subproblem 1
x + -0.84375 = 0.93175322 Simplifying x + -0.84375 = 0.93175322 Reorder the terms: -0.84375 + x = 0.93175322 Solving -0.84375 + x = 0.93175322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.84375' to each side of the equation. -0.84375 + 0.84375 + x = 0.93175322 + 0.84375 Combine like terms: -0.84375 + 0.84375 = 0.00000 0.00000 + x = 0.93175322 + 0.84375 x = 0.93175322 + 0.84375 Combine like terms: 0.93175322 + 0.84375 = 1.77550322 x = 1.77550322 Simplifying x = 1.77550322Subproblem 2
x + -0.84375 = -0.93175322 Simplifying x + -0.84375 = -0.93175322 Reorder the terms: -0.84375 + x = -0.93175322 Solving -0.84375 + x = -0.93175322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.84375' to each side of the equation. -0.84375 + 0.84375 + x = -0.93175322 + 0.84375 Combine like terms: -0.84375 + 0.84375 = 0.00000 0.00000 + x = -0.93175322 + 0.84375 x = -0.93175322 + 0.84375 Combine like terms: -0.93175322 + 0.84375 = -0.08800322 x = -0.08800322 Simplifying x = -0.08800322Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.77550322, -0.08800322}
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