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Simplifying 4x2 + 36x + 64 = 25 Reorder the terms: 64 + 36x + 4x2 = 25 Solving 64 + 36x + 4x2 = 25 Solving for variable 'x'. Reorder the terms: 64 + -25 + 36x + 4x2 = 25 + -25 Combine like terms: 64 + -25 = 39 39 + 36x + 4x2 = 25 + -25 Combine like terms: 25 + -25 = 0 39 + 36x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 9.75 + 9x + x2 = 0 Move the constant term to the right: Add '-9.75' to each side of the equation. 9.75 + 9x + -9.75 + x2 = 0 + -9.75 Reorder the terms: 9.75 + -9.75 + 9x + x2 = 0 + -9.75 Combine like terms: 9.75 + -9.75 = 0.00 0.00 + 9x + x2 = 0 + -9.75 9x + x2 = 0 + -9.75 Combine like terms: 0 + -9.75 = -9.75 9x + x2 = -9.75 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = -9.75 + 20.25 Reorder the terms: 20.25 + 9x + x2 = -9.75 + 20.25 Combine like terms: -9.75 + 20.25 = 10.5 20.25 + 9x + x2 = 10.5 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 10.5 Calculate the square root of the right side: 3.240370349 Break this problem into two subproblems by setting (x + 4.5) equal to 3.240370349 and -3.240370349.Subproblem 1
x + 4.5 = 3.240370349 Simplifying x + 4.5 = 3.240370349 Reorder the terms: 4.5 + x = 3.240370349 Solving 4.5 + x = 3.240370349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 3.240370349 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 3.240370349 + -4.5 x = 3.240370349 + -4.5 Combine like terms: 3.240370349 + -4.5 = -1.259629651 x = -1.259629651 Simplifying x = -1.259629651Subproblem 2
x + 4.5 = -3.240370349 Simplifying x + 4.5 = -3.240370349 Reorder the terms: 4.5 + x = -3.240370349 Solving 4.5 + x = -3.240370349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -3.240370349 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -3.240370349 + -4.5 x = -3.240370349 + -4.5 Combine like terms: -3.240370349 + -4.5 = -7.740370349 x = -7.740370349 Simplifying x = -7.740370349Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.259629651, -7.740370349}
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