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Simplifying 4x2 + -53x + -9 = 0 Reorder the terms: -9 + -53x + 4x2 = 0 Solving -9 + -53x + 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'. -2.25 + -13.25x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -13.25x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -13.25x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -13.25x + x2 = 0 + 2.25 -13.25x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -13.25x + x2 = 2.25 The x term is -13.25x. Take half its coefficient (-6.625). Square it (43.890625) and add it to both sides. Add '43.890625' to each side of the equation. -13.25x + 43.890625 + x2 = 2.25 + 43.890625 Reorder the terms: 43.890625 + -13.25x + x2 = 2.25 + 43.890625 Combine like terms: 2.25 + 43.890625 = 46.140625 43.890625 + -13.25x + x2 = 46.140625 Factor a perfect square on the left side: (x + -6.625)(x + -6.625) = 46.140625 Calculate the square root of the right side: 6.792689085 Break this problem into two subproblems by setting (x + -6.625) equal to 6.792689085 and -6.792689085.Subproblem 1
x + -6.625 = 6.792689085 Simplifying x + -6.625 = 6.792689085 Reorder the terms: -6.625 + x = 6.792689085 Solving -6.625 + x = 6.792689085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.625' to each side of the equation. -6.625 + 6.625 + x = 6.792689085 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + x = 6.792689085 + 6.625 x = 6.792689085 + 6.625 Combine like terms: 6.792689085 + 6.625 = 13.417689085 x = 13.417689085 Simplifying x = 13.417689085Subproblem 2
x + -6.625 = -6.792689085 Simplifying x + -6.625 = -6.792689085 Reorder the terms: -6.625 + x = -6.792689085 Solving -6.625 + x = -6.792689085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.625' to each side of the equation. -6.625 + 6.625 + x = -6.792689085 + 6.625 Combine like terms: -6.625 + 6.625 = 0.000 0.000 + x = -6.792689085 + 6.625 x = -6.792689085 + 6.625 Combine like terms: -6.792689085 + 6.625 = -0.167689085 x = -0.167689085 Simplifying x = -0.167689085Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.417689085, -0.167689085}
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