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Simplifying 4x2 + -13x + -36 = 0 Reorder the terms: -36 + -13x + 4x2 = 0 Solving -36 + -13x + 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 + -3.25x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -3.25x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -3.25x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -3.25x + x2 = 0 + 9 -3.25x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -3.25x + x2 = 9 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 9 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 9 + 2.640625 Combine like terms: 9 + 2.640625 = 11.640625 2.640625 + -3.25x + x2 = 11.640625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 11.640625 Calculate the square root of the right side: 3.411836016 Break this problem into two subproblems by setting (x + -1.625) equal to 3.411836016 and -3.411836016.Subproblem 1
x + -1.625 = 3.411836016 Simplifying x + -1.625 = 3.411836016 Reorder the terms: -1.625 + x = 3.411836016 Solving -1.625 + x = 3.411836016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 3.411836016 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 3.411836016 + 1.625 x = 3.411836016 + 1.625 Combine like terms: 3.411836016 + 1.625 = 5.036836016 x = 5.036836016 Simplifying x = 5.036836016Subproblem 2
x + -1.625 = -3.411836016 Simplifying x + -1.625 = -3.411836016 Reorder the terms: -1.625 + x = -3.411836016 Solving -1.625 + x = -3.411836016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -3.411836016 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -3.411836016 + 1.625 x = -3.411836016 + 1.625 Combine like terms: -3.411836016 + 1.625 = -1.786836016 x = -1.786836016 Simplifying x = -1.786836016Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.036836016, -1.786836016}
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