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Simplifying 210x2 + -1980x + 7700 = 6230 Reorder the terms: 7700 + -1980x + 210x2 = 6230 Solving 7700 + -1980x + 210x2 = 6230 Solving for variable 'x'. Reorder the terms: 7700 + -6230 + -1980x + 210x2 = 6230 + -6230 Combine like terms: 7700 + -6230 = 1470 1470 + -1980x + 210x2 = 6230 + -6230 Combine like terms: 6230 + -6230 = 0 1470 + -1980x + 210x2 = 0 Factor out the Greatest Common Factor (GCF), '30'. 30(49 + -66x + 7x2) = 0 Ignore the factor 30.Subproblem 1
Set the factor '(49 + -66x + 7x2)' equal to zero and attempt to solve: Simplifying 49 + -66x + 7x2 = 0 Solving 49 + -66x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 7 + -9.428571429x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -9.428571429x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -9.428571429x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -9.428571429x + x2 = 0 + -7 -9.428571429x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -9.428571429x + x2 = -7 The x term is -9.428571429x. Take half its coefficient (-4.714285715). Square it (22.22448980) and add it to both sides. Add '22.22448980' to each side of the equation. -9.428571429x + 22.22448980 + x2 = -7 + 22.22448980 Reorder the terms: 22.22448980 + -9.428571429x + x2 = -7 + 22.22448980 Combine like terms: -7 + 22.22448980 = 15.2244898 22.22448980 + -9.428571429x + x2 = 15.2244898 Factor a perfect square on the left side: (x + -4.714285715)(x + -4.714285715) = 15.2244898 Calculate the square root of the right side: 3.901857224 Break this problem into two subproblems by setting (x + -4.714285715) equal to 3.901857224 and -3.901857224.Subproblem 1
x + -4.714285715 = 3.901857224 Simplifying x + -4.714285715 = 3.901857224 Reorder the terms: -4.714285715 + x = 3.901857224 Solving -4.714285715 + x = 3.901857224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.714285715' to each side of the equation. -4.714285715 + 4.714285715 + x = 3.901857224 + 4.714285715 Combine like terms: -4.714285715 + 4.714285715 = 0.000000000 0.000000000 + x = 3.901857224 + 4.714285715 x = 3.901857224 + 4.714285715 Combine like terms: 3.901857224 + 4.714285715 = 8.616142939 x = 8.616142939 Simplifying x = 8.616142939Subproblem 2
x + -4.714285715 = -3.901857224 Simplifying x + -4.714285715 = -3.901857224 Reorder the terms: -4.714285715 + x = -3.901857224 Solving -4.714285715 + x = -3.901857224 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.714285715' to each side of the equation. -4.714285715 + 4.714285715 + x = -3.901857224 + 4.714285715 Combine like terms: -4.714285715 + 4.714285715 = 0.000000000 0.000000000 + x = -3.901857224 + 4.714285715 x = -3.901857224 + 4.714285715 Combine like terms: -3.901857224 + 4.714285715 = 0.812428491 x = 0.812428491 Simplifying x = 0.812428491Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.616142939, 0.812428491}Solution
x = {8.616142939, 0.812428491}
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