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Simplifying 7x2 + -53x + -21 = 0 Reorder the terms: -21 + -53x + 7x2 = 0 Solving -21 + -53x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3 + -7.571428571x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -7.571428571x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -7.571428571x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7.571428571x + x2 = 0 + 3 -7.571428571x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -7.571428571x + x2 = 3 The x term is -7.571428571x. Take half its coefficient (-3.785714286). Square it (14.33163266) and add it to both sides. Add '14.33163266' to each side of the equation. -7.571428571x + 14.33163266 + x2 = 3 + 14.33163266 Reorder the terms: 14.33163266 + -7.571428571x + x2 = 3 + 14.33163266 Combine like terms: 3 + 14.33163266 = 17.33163266 14.33163266 + -7.571428571x + x2 = 17.33163266 Factor a perfect square on the left side: (x + -3.785714286)(x + -3.785714286) = 17.33163266 Calculate the square root of the right side: 4.16312775 Break this problem into two subproblems by setting (x + -3.785714286) equal to 4.16312775 and -4.16312775.Subproblem 1
x + -3.785714286 = 4.16312775 Simplifying x + -3.785714286 = 4.16312775 Reorder the terms: -3.785714286 + x = 4.16312775 Solving -3.785714286 + x = 4.16312775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.785714286' to each side of the equation. -3.785714286 + 3.785714286 + x = 4.16312775 + 3.785714286 Combine like terms: -3.785714286 + 3.785714286 = 0.000000000 0.000000000 + x = 4.16312775 + 3.785714286 x = 4.16312775 + 3.785714286 Combine like terms: 4.16312775 + 3.785714286 = 7.948842036 x = 7.948842036 Simplifying x = 7.948842036Subproblem 2
x + -3.785714286 = -4.16312775 Simplifying x + -3.785714286 = -4.16312775 Reorder the terms: -3.785714286 + x = -4.16312775 Solving -3.785714286 + x = -4.16312775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.785714286' to each side of the equation. -3.785714286 + 3.785714286 + x = -4.16312775 + 3.785714286 Combine like terms: -3.785714286 + 3.785714286 = 0.000000000 0.000000000 + x = -4.16312775 + 3.785714286 x = -4.16312775 + 3.785714286 Combine like terms: -4.16312775 + 3.785714286 = -0.377413464 x = -0.377413464 Simplifying x = -0.377413464Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.948842036, -0.377413464}
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