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Simplifying 0.3x2 + -15x + 94 = 0 Reorder the terms: 94 + -15x + 0.3x2 = 0 Solving 94 + -15x + 0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.3 the coefficient of the squared term: Divide each side by '0.3'. 313.3333333 + -50x + x2 = 0 Move the constant term to the right: Add '-313.3333333' to each side of the equation. 313.3333333 + -50x + -313.3333333 + x2 = 0 + -313.3333333 Reorder the terms: 313.3333333 + -313.3333333 + -50x + x2 = 0 + -313.3333333 Combine like terms: 313.3333333 + -313.3333333 = 0.0000000 0.0000000 + -50x + x2 = 0 + -313.3333333 -50x + x2 = 0 + -313.3333333 Combine like terms: 0 + -313.3333333 = -313.3333333 -50x + x2 = -313.3333333 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -313.3333333 + 625 Reorder the terms: 625 + -50x + x2 = -313.3333333 + 625 Combine like terms: -313.3333333 + 625 = 311.6666667 625 + -50x + x2 = 311.6666667 Factor a perfect square on the left side: (x + -25)(x + -25) = 311.6666667 Calculate the square root of the right side: 17.65408357 Break this problem into two subproblems by setting (x + -25) equal to 17.65408357 and -17.65408357.Subproblem 1
x + -25 = 17.65408357 Simplifying x + -25 = 17.65408357 Reorder the terms: -25 + x = 17.65408357 Solving -25 + x = 17.65408357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 17.65408357 + 25 Combine like terms: -25 + 25 = 0 0 + x = 17.65408357 + 25 x = 17.65408357 + 25 Combine like terms: 17.65408357 + 25 = 42.65408357 x = 42.65408357 Simplifying x = 42.65408357Subproblem 2
x + -25 = -17.65408357 Simplifying x + -25 = -17.65408357 Reorder the terms: -25 + x = -17.65408357 Solving -25 + x = -17.65408357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -17.65408357 + 25 Combine like terms: -25 + 25 = 0 0 + x = -17.65408357 + 25 x = -17.65408357 + 25 Combine like terms: -17.65408357 + 25 = 7.34591643 x = 7.34591643 Simplifying x = 7.34591643Solution
The solution to the problem is based on the solutions from the subproblems. x = {42.65408357, 7.34591643}
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