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Simplifying 3x2 + -120x + 2.5 = 0 Reorder the terms: 2.5 + -120x + 3x2 = 0 Solving 2.5 + -120x + 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'. 0.8333333333 + -40x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -40x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -40x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -40x + x2 = 0 + -0.8333333333 -40x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -40x + x2 = -0.8333333333 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -0.8333333333 + 400 Reorder the terms: 400 + -40x + x2 = -0.8333333333 + 400 Combine like terms: -0.8333333333 + 400 = 399.1666666667 400 + -40x + x2 = 399.1666666667 Factor a perfect square on the left side: (x + -20)(x + -20) = 399.1666666667 Calculate the square root of the right side: 19.979155805 Break this problem into two subproblems by setting (x + -20) equal to 19.979155805 and -19.979155805.Subproblem 1
x + -20 = 19.979155805 Simplifying x + -20 = 19.979155805 Reorder the terms: -20 + x = 19.979155805 Solving -20 + x = 19.979155805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 19.979155805 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.979155805 + 20 x = 19.979155805 + 20 Combine like terms: 19.979155805 + 20 = 39.979155805 x = 39.979155805 Simplifying x = 39.979155805Subproblem 2
x + -20 = -19.979155805 Simplifying x + -20 = -19.979155805 Reorder the terms: -20 + x = -19.979155805 Solving -20 + x = -19.979155805 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -19.979155805 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.979155805 + 20 x = -19.979155805 + 20 Combine like terms: -19.979155805 + 20 = 0.020844195 x = 0.020844195 Simplifying x = 0.020844195Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.979155805, 0.020844195}
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