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Simplifying 4x2 + 57x + -1445 = 0 Reorder the terms: -1445 + 57x + 4x2 = 0 Solving -1445 + 57x + 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'. -361.25 + 14.25x + x2 = 0 Move the constant term to the right: Add '361.25' to each side of the equation. -361.25 + 14.25x + 361.25 + x2 = 0 + 361.25 Reorder the terms: -361.25 + 361.25 + 14.25x + x2 = 0 + 361.25 Combine like terms: -361.25 + 361.25 = 0.00 0.00 + 14.25x + x2 = 0 + 361.25 14.25x + x2 = 0 + 361.25 Combine like terms: 0 + 361.25 = 361.25 14.25x + x2 = 361.25 The x term is 14.25x. Take half its coefficient (7.125). Square it (50.765625) and add it to both sides. Add '50.765625' to each side of the equation. 14.25x + 50.765625 + x2 = 361.25 + 50.765625 Reorder the terms: 50.765625 + 14.25x + x2 = 361.25 + 50.765625 Combine like terms: 361.25 + 50.765625 = 412.015625 50.765625 + 14.25x + x2 = 412.015625 Factor a perfect square on the left side: (x + 7.125)(x + 7.125) = 412.015625 Calculate the square root of the right side: 20.298168021 Break this problem into two subproblems by setting (x + 7.125) equal to 20.298168021 and -20.298168021.Subproblem 1
x + 7.125 = 20.298168021 Simplifying x + 7.125 = 20.298168021 Reorder the terms: 7.125 + x = 20.298168021 Solving 7.125 + x = 20.298168021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.125' to each side of the equation. 7.125 + -7.125 + x = 20.298168021 + -7.125 Combine like terms: 7.125 + -7.125 = 0.000 0.000 + x = 20.298168021 + -7.125 x = 20.298168021 + -7.125 Combine like terms: 20.298168021 + -7.125 = 13.173168021 x = 13.173168021 Simplifying x = 13.173168021Subproblem 2
x + 7.125 = -20.298168021 Simplifying x + 7.125 = -20.298168021 Reorder the terms: 7.125 + x = -20.298168021 Solving 7.125 + x = -20.298168021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.125' to each side of the equation. 7.125 + -7.125 + x = -20.298168021 + -7.125 Combine like terms: 7.125 + -7.125 = 0.000 0.000 + x = -20.298168021 + -7.125 x = -20.298168021 + -7.125 Combine like terms: -20.298168021 + -7.125 = -27.423168021 x = -27.423168021 Simplifying x = -27.423168021Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.173168021, -27.423168021}
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