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Simplifying -1x2 + 20x + 60 = 0 Reorder the terms: 60 + 20x + -1x2 = 0 Solving 60 + 20x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -60 + -20x + x2 = 0 Move the constant term to the right: Add '60' to each side of the equation. -60 + -20x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -20x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -20x + x2 = 0 + 60 -20x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -20x + x2 = 60 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 60 + 100 Reorder the terms: 100 + -20x + x2 = 60 + 100 Combine like terms: 60 + 100 = 160 100 + -20x + x2 = 160 Factor a perfect square on the left side: (x + -10)(x + -10) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (x + -10) equal to 12.649110641 and -12.649110641.Subproblem 1
x + -10 = 12.649110641 Simplifying x + -10 = 12.649110641 Reorder the terms: -10 + x = 12.649110641 Solving -10 + x = 12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 12.649110641 + 10 Combine like terms: -10 + 10 = 0 0 + x = 12.649110641 + 10 x = 12.649110641 + 10 Combine like terms: 12.649110641 + 10 = 22.649110641 x = 22.649110641 Simplifying x = 22.649110641Subproblem 2
x + -10 = -12.649110641 Simplifying x + -10 = -12.649110641 Reorder the terms: -10 + x = -12.649110641 Solving -10 + x = -12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -12.649110641 + 10 Combine like terms: -10 + 10 = 0 0 + x = -12.649110641 + 10 x = -12.649110641 + 10 Combine like terms: -12.649110641 + 10 = -2.649110641 x = -2.649110641 Simplifying x = -2.649110641Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.649110641, -2.649110641}
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