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Simplifying 300x2 + -240x + 32 = 0 Reorder the terms: 32 + -240x + 300x2 = 0 Solving 32 + -240x + 300x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(8 + -60x + 75x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(8 + -60x + 75x2)' equal to zero and attempt to solve: Simplifying 8 + -60x + 75x2 = 0 Solving 8 + -60x + 75x2 = 0 Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. 0.1066666667 + -0.8x + x2 = 0 Move the constant term to the right: Add '-0.1066666667' to each side of the equation. 0.1066666667 + -0.8x + -0.1066666667 + x2 = 0 + -0.1066666667 Reorder the terms: 0.1066666667 + -0.1066666667 + -0.8x + x2 = 0 + -0.1066666667 Combine like terms: 0.1066666667 + -0.1066666667 = 0.0000000000 0.0000000000 + -0.8x + x2 = 0 + -0.1066666667 -0.8x + x2 = 0 + -0.1066666667 Combine like terms: 0 + -0.1066666667 = -0.1066666667 -0.8x + x2 = -0.1066666667 The x term is -0.8x. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x + 0.16 + x2 = -0.1066666667 + 0.16 Reorder the terms: 0.16 + -0.8x + x2 = -0.1066666667 + 0.16 Combine like terms: -0.1066666667 + 0.16 = 0.0533333333 0.16 + -0.8x + x2 = 0.0533333333 Factor a perfect square on the left side: (x + -0.4)(x + -0.4) = 0.0533333333 Calculate the square root of the right side: 0.230940108 Break this problem into two subproblems by setting (x + -0.4) equal to 0.230940108 and -0.230940108.Subproblem 1
x + -0.4 = 0.230940108 Simplifying x + -0.4 = 0.230940108 Reorder the terms: -0.4 + x = 0.230940108 Solving -0.4 + x = 0.230940108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 0.230940108 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 0.230940108 + 0.4 x = 0.230940108 + 0.4 Combine like terms: 0.230940108 + 0.4 = 0.630940108 x = 0.630940108 Simplifying x = 0.630940108Subproblem 2
x + -0.4 = -0.230940108 Simplifying x + -0.4 = -0.230940108 Reorder the terms: -0.4 + x = -0.230940108 Solving -0.4 + x = -0.230940108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -0.230940108 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -0.230940108 + 0.4 x = -0.230940108 + 0.4 Combine like terms: -0.230940108 + 0.4 = 0.169059892 x = 0.169059892 Simplifying x = 0.169059892Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.630940108, 0.169059892}Solution
x = {0.630940108, 0.169059892}
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