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Simplifying 75x2 + 60x + 8 = 0 Reorder the terms: 8 + 60x + 75x2 = 0 Solving 8 + 60x + 75x2 = 0 Solving for variable 'x'. 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 = -0.169059892 x = -0.169059892 Simplifying x = -0.169059892Subproblem 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 = -0.630940108 x = -0.630940108 Simplifying x = -0.630940108Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.169059892, -0.630940108}
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