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Simplifying 4x2 + -25x + -36 = 0 Reorder the terms: -36 + -25x + 4x2 = 0 Solving -36 + -25x + 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'. -9 + -6.25x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -6.25x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -6.25x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -6.25x + x2 = 0 + 9 -6.25x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -6.25x + x2 = 9 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 9 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 9 + 9.765625 Combine like terms: 9 + 9.765625 = 18.765625 9.765625 + -6.25x + x2 = 18.765625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 18.765625 Calculate the square root of the right side: 4.331930863 Break this problem into two subproblems by setting (x + -3.125) equal to 4.331930863 and -4.331930863.Subproblem 1
x + -3.125 = 4.331930863 Simplifying x + -3.125 = 4.331930863 Reorder the terms: -3.125 + x = 4.331930863 Solving -3.125 + x = 4.331930863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 4.331930863 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 4.331930863 + 3.125 x = 4.331930863 + 3.125 Combine like terms: 4.331930863 + 3.125 = 7.456930863 x = 7.456930863 Simplifying x = 7.456930863Subproblem 2
x + -3.125 = -4.331930863 Simplifying x + -3.125 = -4.331930863 Reorder the terms: -3.125 + x = -4.331930863 Solving -3.125 + x = -4.331930863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -4.331930863 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -4.331930863 + 3.125 x = -4.331930863 + 3.125 Combine like terms: -4.331930863 + 3.125 = -1.206930863 x = -1.206930863 Simplifying x = -1.206930863Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.456930863, -1.206930863}
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