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Simplifying 4x2 + -61x + 128 = 0 Reorder the terms: 128 + -61x + 4x2 = 0 Solving 128 + -61x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 32 + -15.25x + x2 = 0 Move the constant term to the right: Add '-32' to each side of the equation. 32 + -15.25x + -32 + x2 = 0 + -32 Reorder the terms: 32 + -32 + -15.25x + x2 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -15.25x + x2 = 0 + -32 -15.25x + x2 = 0 + -32 Combine like terms: 0 + -32 = -32 -15.25x + x2 = -32 The x term is -15.25x. Take half its coefficient (-7.625). Square it (58.140625) and add it to both sides. Add '58.140625' to each side of the equation. -15.25x + 58.140625 + x2 = -32 + 58.140625 Reorder the terms: 58.140625 + -15.25x + x2 = -32 + 58.140625 Combine like terms: -32 + 58.140625 = 26.140625 58.140625 + -15.25x + x2 = 26.140625 Factor a perfect square on the left side: (x + -7.625)(x + -7.625) = 26.140625 Calculate the square root of the right side: 5.112790334 Break this problem into two subproblems by setting (x + -7.625) equal to 5.112790334 and -5.112790334.Subproblem 1
x + -7.625 = 5.112790334 Simplifying x + -7.625 = 5.112790334 Reorder the terms: -7.625 + x = 5.112790334 Solving -7.625 + x = 5.112790334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.625' to each side of the equation. -7.625 + 7.625 + x = 5.112790334 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + x = 5.112790334 + 7.625 x = 5.112790334 + 7.625 Combine like terms: 5.112790334 + 7.625 = 12.737790334 x = 12.737790334 Simplifying x = 12.737790334Subproblem 2
x + -7.625 = -5.112790334 Simplifying x + -7.625 = -5.112790334 Reorder the terms: -7.625 + x = -5.112790334 Solving -7.625 + x = -5.112790334 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.625' to each side of the equation. -7.625 + 7.625 + x = -5.112790334 + 7.625 Combine like terms: -7.625 + 7.625 = 0.000 0.000 + x = -5.112790334 + 7.625 x = -5.112790334 + 7.625 Combine like terms: -5.112790334 + 7.625 = 2.512209666 x = 2.512209666 Simplifying x = 2.512209666Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.737790334, 2.512209666}
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