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Simplifying 32x2 + -100x + 5 = 0 Reorder the terms: 5 + -100x + 32x2 = 0 Solving 5 + -100x + 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 + -3.125x + x2 = 0 Move the constant term to the right: Add '-0.15625' to each side of the equation. 0.15625 + -3.125x + -0.15625 + x2 = 0 + -0.15625 Reorder the terms: 0.15625 + -0.15625 + -3.125x + x2 = 0 + -0.15625 Combine like terms: 0.15625 + -0.15625 = 0.00000 0.00000 + -3.125x + x2 = 0 + -0.15625 -3.125x + x2 = 0 + -0.15625 Combine like terms: 0 + -0.15625 = -0.15625 -3.125x + x2 = -0.15625 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = -0.15625 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = -0.15625 + 2.44140625 Combine like terms: -0.15625 + 2.44140625 = 2.28515625 2.44140625 + -3.125x + x2 = 2.28515625 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 2.28515625 Calculate the square root of the right side: 1.511673328 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.511673328 and -1.511673328.Subproblem 1
x + -1.5625 = 1.511673328 Simplifying x + -1.5625 = 1.511673328 Reorder the terms: -1.5625 + x = 1.511673328 Solving -1.5625 + x = 1.511673328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 1.511673328 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.511673328 + 1.5625 x = 1.511673328 + 1.5625 Combine like terms: 1.511673328 + 1.5625 = 3.074173328 x = 3.074173328 Simplifying x = 3.074173328Subproblem 2
x + -1.5625 = -1.511673328 Simplifying x + -1.5625 = -1.511673328 Reorder the terms: -1.5625 + x = -1.511673328 Solving -1.5625 + x = -1.511673328 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -1.511673328 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.511673328 + 1.5625 x = -1.511673328 + 1.5625 Combine like terms: -1.511673328 + 1.5625 = 0.050826672 x = 0.050826672 Simplifying x = 0.050826672Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.074173328, 0.050826672}
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