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Simplifying (4x2 + 17x + -40) = 0 Reorder the terms: (-40 + 17x + 4x2) = 0 Remove parenthesis around (-40 + 17x + 4x2) -40 + 17x + 4x2 = 0 Solving -40 + 17x + 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'. -10 + 4.25x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 4.25x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 4.25x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 4.25x + x2 = 0 + 10 4.25x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 4.25x + x2 = 10 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 10 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 10 + 4.515625 Combine like terms: 10 + 4.515625 = 14.515625 4.515625 + 4.25x + x2 = 14.515625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 14.515625 Calculate the square root of the right side: 3.809937664 Break this problem into two subproblems by setting (x + 2.125) equal to 3.809937664 and -3.809937664.Subproblem 1
x + 2.125 = 3.809937664 Simplifying x + 2.125 = 3.809937664 Reorder the terms: 2.125 + x = 3.809937664 Solving 2.125 + x = 3.809937664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 3.809937664 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 3.809937664 + -2.125 x = 3.809937664 + -2.125 Combine like terms: 3.809937664 + -2.125 = 1.684937664 x = 1.684937664 Simplifying x = 1.684937664Subproblem 2
x + 2.125 = -3.809937664 Simplifying x + 2.125 = -3.809937664 Reorder the terms: 2.125 + x = -3.809937664 Solving 2.125 + x = -3.809937664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -3.809937664 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -3.809937664 + -2.125 x = -3.809937664 + -2.125 Combine like terms: -3.809937664 + -2.125 = -5.934937664 x = -5.934937664 Simplifying x = -5.934937664Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.684937664, -5.934937664}
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