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Simplifying -68x2 + 4200x + -5320 = 0 Reorder the terms: -5320 + 4200x + -68x2 = 0 Solving -5320 + 4200x + -68x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-1330 + 1050x + -17x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1330 + 1050x + -17x2)' equal to zero and attempt to solve: Simplifying -1330 + 1050x + -17x2 = 0 Solving -1330 + 1050x + -17x2 = 0 Begin completing the square. Divide all terms by -17 the coefficient of the squared term: Divide each side by '-17'. 78.23529412 + -61.76470588x + x2 = 0 Move the constant term to the right: Add '-78.23529412' to each side of the equation. 78.23529412 + -61.76470588x + -78.23529412 + x2 = 0 + -78.23529412 Reorder the terms: 78.23529412 + -78.23529412 + -61.76470588x + x2 = 0 + -78.23529412 Combine like terms: 78.23529412 + -78.23529412 = 0.00000000 0.00000000 + -61.76470588x + x2 = 0 + -78.23529412 -61.76470588x + x2 = 0 + -78.23529412 Combine like terms: 0 + -78.23529412 = -78.23529412 -61.76470588x + x2 = -78.23529412 The x term is -61.76470588x. Take half its coefficient (-30.88235294). Square it (953.7197231) and add it to both sides. Add '953.7197231' to each side of the equation. -61.76470588x + 953.7197231 + x2 = -78.23529412 + 953.7197231 Reorder the terms: 953.7197231 + -61.76470588x + x2 = -78.23529412 + 953.7197231 Combine like terms: -78.23529412 + 953.7197231 = 875.48442898 953.7197231 + -61.76470588x + x2 = 875.48442898 Factor a perfect square on the left side: (x + -30.88235294)(x + -30.88235294) = 875.48442898 Calculate the square root of the right side: 29.588586127 Break this problem into two subproblems by setting (x + -30.88235294) equal to 29.588586127 and -29.588586127.Subproblem 1
x + -30.88235294 = 29.588586127 Simplifying x + -30.88235294 = 29.588586127 Reorder the terms: -30.88235294 + x = 29.588586127 Solving -30.88235294 + x = 29.588586127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.88235294' to each side of the equation. -30.88235294 + 30.88235294 + x = 29.588586127 + 30.88235294 Combine like terms: -30.88235294 + 30.88235294 = 0.00000000 0.00000000 + x = 29.588586127 + 30.88235294 x = 29.588586127 + 30.88235294 Combine like terms: 29.588586127 + 30.88235294 = 60.470939067 x = 60.470939067 Simplifying x = 60.470939067Subproblem 2
x + -30.88235294 = -29.588586127 Simplifying x + -30.88235294 = -29.588586127 Reorder the terms: -30.88235294 + x = -29.588586127 Solving -30.88235294 + x = -29.588586127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.88235294' to each side of the equation. -30.88235294 + 30.88235294 + x = -29.588586127 + 30.88235294 Combine like terms: -30.88235294 + 30.88235294 = 0.00000000 0.00000000 + x = -29.588586127 + 30.88235294 x = -29.588586127 + 30.88235294 Combine like terms: -29.588586127 + 30.88235294 = 1.293766813 x = 1.293766813 Simplifying x = 1.293766813Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.470939067, 1.293766813}Solution
x = {60.470939067, 1.293766813}
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