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Simplifying 0 = 2x2 + -21x + -40 Reorder the terms: 0 = -40 + -21x + 2x2 Solving 0 = -40 + -21x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 40 = 40 40 + 21x + -2x2 = -40 + -21x + 2x2 + 40 + 21x + -2x2 Reorder the terms: 40 + 21x + -2x2 = -40 + 40 + -21x + 21x + 2x2 + -2x2 Combine like terms: -40 + 40 = 0 40 + 21x + -2x2 = 0 + -21x + 21x + 2x2 + -2x2 40 + 21x + -2x2 = -21x + 21x + 2x2 + -2x2 Combine like terms: -21x + 21x = 0 40 + 21x + -2x2 = 0 + 2x2 + -2x2 40 + 21x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 40 + 21x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -20 + -10.5x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -10.5x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -10.5x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -10.5x + x2 = 0 + 20 -10.5x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -10.5x + x2 = 20 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = 20 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = 20 + 27.5625 Combine like terms: 20 + 27.5625 = 47.5625 27.5625 + -10.5x + x2 = 47.5625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 47.5625 Calculate the square root of the right side: 6.896557112 Break this problem into two subproblems by setting (x + -5.25) equal to 6.896557112 and -6.896557112.Subproblem 1
x + -5.25 = 6.896557112 Simplifying x + -5.25 = 6.896557112 Reorder the terms: -5.25 + x = 6.896557112 Solving -5.25 + x = 6.896557112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 6.896557112 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 6.896557112 + 5.25 x = 6.896557112 + 5.25 Combine like terms: 6.896557112 + 5.25 = 12.146557112 x = 12.146557112 Simplifying x = 12.146557112Subproblem 2
x + -5.25 = -6.896557112 Simplifying x + -5.25 = -6.896557112 Reorder the terms: -5.25 + x = -6.896557112 Solving -5.25 + x = -6.896557112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -6.896557112 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -6.896557112 + 5.25 x = -6.896557112 + 5.25 Combine like terms: -6.896557112 + 5.25 = -1.646557112 x = -1.646557112 Simplifying x = -1.646557112Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.146557112, -1.646557112}
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