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Simplifying -3x2 + 60x + 5 = 0 Reorder the terms: 5 + 60x + -3x2 = 0 Solving 5 + 60x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.666666667 + -20x + x2 = 0 Move the constant term to the right: Add '1.666666667' to each side of the equation. -1.666666667 + -20x + 1.666666667 + x2 = 0 + 1.666666667 Reorder the terms: -1.666666667 + 1.666666667 + -20x + x2 = 0 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + -20x + x2 = 0 + 1.666666667 -20x + x2 = 0 + 1.666666667 Combine like terms: 0 + 1.666666667 = 1.666666667 -20x + x2 = 1.666666667 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 = 1.666666667 + 100 Reorder the terms: 100 + -20x + x2 = 1.666666667 + 100 Combine like terms: 1.666666667 + 100 = 101.666666667 100 + -20x + x2 = 101.666666667 Factor a perfect square on the left side: (x + -10)(x + -10) = 101.666666667 Calculate the square root of the right side: 10.082988975 Break this problem into two subproblems by setting (x + -10) equal to 10.082988975 and -10.082988975.Subproblem 1
x + -10 = 10.082988975 Simplifying x + -10 = 10.082988975 Reorder the terms: -10 + x = 10.082988975 Solving -10 + x = 10.082988975 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 = 10.082988975 + 10 Combine like terms: -10 + 10 = 0 0 + x = 10.082988975 + 10 x = 10.082988975 + 10 Combine like terms: 10.082988975 + 10 = 20.082988975 x = 20.082988975 Simplifying x = 20.082988975Subproblem 2
x + -10 = -10.082988975 Simplifying x + -10 = -10.082988975 Reorder the terms: -10 + x = -10.082988975 Solving -10 + x = -10.082988975 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 = -10.082988975 + 10 Combine like terms: -10 + 10 = 0 0 + x = -10.082988975 + 10 x = -10.082988975 + 10 Combine like terms: -10.082988975 + 10 = -0.082988975 x = -0.082988975 Simplifying x = -0.082988975Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.082988975, -0.082988975}
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