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Simplifying -32x2 + -50x + 45 = 0 Reorder the terms: 45 + -50x + -32x2 = 0 Solving 45 + -50x + -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'. -1.40625 + 1.5625x + x2 = 0 Move the constant term to the right: Add '1.40625' to each side of the equation. -1.40625 + 1.5625x + 1.40625 + x2 = 0 + 1.40625 Reorder the terms: -1.40625 + 1.40625 + 1.5625x + x2 = 0 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + 1.5625x + x2 = 0 + 1.40625 1.5625x + x2 = 0 + 1.40625 Combine like terms: 0 + 1.40625 = 1.40625 1.5625x + x2 = 1.40625 The x term is 1.5625x. Take half its coefficient (0.78125). Square it (0.6103515625) and add it to both sides. Add '0.6103515625' to each side of the equation. 1.5625x + 0.6103515625 + x2 = 1.40625 + 0.6103515625 Reorder the terms: 0.6103515625 + 1.5625x + x2 = 1.40625 + 0.6103515625 Combine like terms: 1.40625 + 0.6103515625 = 2.0166015625 0.6103515625 + 1.5625x + x2 = 2.0166015625 Factor a perfect square on the left side: (x + 0.78125)(x + 0.78125) = 2.0166015625 Calculate the square root of the right side: 1.420070971 Break this problem into two subproblems by setting (x + 0.78125) equal to 1.420070971 and -1.420070971.Subproblem 1
x + 0.78125 = 1.420070971 Simplifying x + 0.78125 = 1.420070971 Reorder the terms: 0.78125 + x = 1.420070971 Solving 0.78125 + x = 1.420070971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + x = 1.420070971 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + x = 1.420070971 + -0.78125 x = 1.420070971 + -0.78125 Combine like terms: 1.420070971 + -0.78125 = 0.638820971 x = 0.638820971 Simplifying x = 0.638820971Subproblem 2
x + 0.78125 = -1.420070971 Simplifying x + 0.78125 = -1.420070971 Reorder the terms: 0.78125 + x = -1.420070971 Solving 0.78125 + x = -1.420070971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.78125' to each side of the equation. 0.78125 + -0.78125 + x = -1.420070971 + -0.78125 Combine like terms: 0.78125 + -0.78125 = 0.00000 0.00000 + x = -1.420070971 + -0.78125 x = -1.420070971 + -0.78125 Combine like terms: -1.420070971 + -0.78125 = -2.201320971 x = -2.201320971 Simplifying x = -2.201320971Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.638820971, -2.201320971}
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