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Simplifying -6x2 + 564x + -1750 = 0 Reorder the terms: -1750 + 564x + -6x2 = 0 Solving -1750 + 564x + -6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-875 + 282x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-875 + 282x + -3x2)' equal to zero and attempt to solve: Simplifying -875 + 282x + -3x2 = 0 Solving -875 + 282x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 291.6666667 + -94x + x2 = 0 Move the constant term to the right: Add '-291.6666667' to each side of the equation. 291.6666667 + -94x + -291.6666667 + x2 = 0 + -291.6666667 Reorder the terms: 291.6666667 + -291.6666667 + -94x + x2 = 0 + -291.6666667 Combine like terms: 291.6666667 + -291.6666667 = 0.0000000 0.0000000 + -94x + x2 = 0 + -291.6666667 -94x + x2 = 0 + -291.6666667 Combine like terms: 0 + -291.6666667 = -291.6666667 -94x + x2 = -291.6666667 The x term is -94x. Take half its coefficient (-47). Square it (2209) and add it to both sides. Add '2209' to each side of the equation. -94x + 2209 + x2 = -291.6666667 + 2209 Reorder the terms: 2209 + -94x + x2 = -291.6666667 + 2209 Combine like terms: -291.6666667 + 2209 = 1917.3333333 2209 + -94x + x2 = 1917.3333333 Factor a perfect square on the left side: (x + -47)(x + -47) = 1917.3333333 Calculate the square root of the right side: 43.787364996 Break this problem into two subproblems by setting (x + -47) equal to 43.787364996 and -43.787364996.Subproblem 1
x + -47 = 43.787364996 Simplifying x + -47 = 43.787364996 Reorder the terms: -47 + x = 43.787364996 Solving -47 + x = 43.787364996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47' to each side of the equation. -47 + 47 + x = 43.787364996 + 47 Combine like terms: -47 + 47 = 0 0 + x = 43.787364996 + 47 x = 43.787364996 + 47 Combine like terms: 43.787364996 + 47 = 90.787364996 x = 90.787364996 Simplifying x = 90.787364996Subproblem 2
x + -47 = -43.787364996 Simplifying x + -47 = -43.787364996 Reorder the terms: -47 + x = -43.787364996 Solving -47 + x = -43.787364996 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '47' to each side of the equation. -47 + 47 + x = -43.787364996 + 47 Combine like terms: -47 + 47 = 0 0 + x = -43.787364996 + 47 x = -43.787364996 + 47 Combine like terms: -43.787364996 + 47 = 3.212635004 x = 3.212635004 Simplifying x = 3.212635004Solution
The solution to the problem is based on the solutions from the subproblems. x = {90.787364996, 3.212635004}Solution
x = {90.787364996, 3.212635004}
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