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Simplifying 15.3752x2 + -20.3752x + 6 = 0 Reorder the terms: 6 + -20.3752x + 15.3752x2 = 0 Solving 6 + -20.3752x + 15.3752x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15.3752 the coefficient of the squared term: Divide each side by '15.3752'. 0.3902388262 + -1.325199022x + x2 = 0 Move the constant term to the right: Add '-0.3902388262' to each side of the equation. 0.3902388262 + -1.325199022x + -0.3902388262 + x2 = 0 + -0.3902388262 Reorder the terms: 0.3902388262 + -0.3902388262 + -1.325199022x + x2 = 0 + -0.3902388262 Combine like terms: 0.3902388262 + -0.3902388262 = 0.0000000000 0.0000000000 + -1.325199022x + x2 = 0 + -0.3902388262 -1.325199022x + x2 = 0 + -0.3902388262 Combine like terms: 0 + -0.3902388262 = -0.3902388262 -1.325199022x + x2 = -0.3902388262 The x term is -1.325199022x. Take half its coefficient (-0.662599511). Square it (0.4390381120) and add it to both sides. Add '0.4390381120' to each side of the equation. -1.325199022x + 0.4390381120 + x2 = -0.3902388262 + 0.4390381120 Reorder the terms: 0.4390381120 + -1.325199022x + x2 = -0.3902388262 + 0.4390381120 Combine like terms: -0.3902388262 + 0.4390381120 = 0.0487992858 0.4390381120 + -1.325199022x + x2 = 0.0487992858 Factor a perfect square on the left side: (x + -0.662599511)(x + -0.662599511) = 0.0487992858 Calculate the square root of the right side: 0.220905604 Break this problem into two subproblems by setting (x + -0.662599511) equal to 0.220905604 and -0.220905604.Subproblem 1
x + -0.662599511 = 0.220905604 Simplifying x + -0.662599511 = 0.220905604 Reorder the terms: -0.662599511 + x = 0.220905604 Solving -0.662599511 + x = 0.220905604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.662599511' to each side of the equation. -0.662599511 + 0.662599511 + x = 0.220905604 + 0.662599511 Combine like terms: -0.662599511 + 0.662599511 = 0.000000000 0.000000000 + x = 0.220905604 + 0.662599511 x = 0.220905604 + 0.662599511 Combine like terms: 0.220905604 + 0.662599511 = 0.883505115 x = 0.883505115 Simplifying x = 0.883505115Subproblem 2
x + -0.662599511 = -0.220905604 Simplifying x + -0.662599511 = -0.220905604 Reorder the terms: -0.662599511 + x = -0.220905604 Solving -0.662599511 + x = -0.220905604 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.662599511' to each side of the equation. -0.662599511 + 0.662599511 + x = -0.220905604 + 0.662599511 Combine like terms: -0.662599511 + 0.662599511 = 0.000000000 0.000000000 + x = -0.220905604 + 0.662599511 x = -0.220905604 + 0.662599511 Combine like terms: -0.220905604 + 0.662599511 = 0.441693907 x = 0.441693907 Simplifying x = 0.441693907Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.883505115, 0.441693907}
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