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Simplifying -1.4x2 + 30.7x + -101.4 = 0 Reorder the terms: -101.4 + 30.7x + -1.4x2 = 0 Solving -101.4 + 30.7x + -1.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.4 the coefficient of the squared term: Divide each side by '-1.4'. 72.42857143 + -21.92857143x + x2 = 0 Move the constant term to the right: Add '-72.42857143' to each side of the equation. 72.42857143 + -21.92857143x + -72.42857143 + x2 = 0 + -72.42857143 Reorder the terms: 72.42857143 + -72.42857143 + -21.92857143x + x2 = 0 + -72.42857143 Combine like terms: 72.42857143 + -72.42857143 = 0.00000000 0.00000000 + -21.92857143x + x2 = 0 + -72.42857143 -21.92857143x + x2 = 0 + -72.42857143 Combine like terms: 0 + -72.42857143 = -72.42857143 -21.92857143x + x2 = -72.42857143 The x term is -21.92857143x. Take half its coefficient (-10.96428572). Square it (120.2155614) and add it to both sides. Add '120.2155614' to each side of the equation. -21.92857143x + 120.2155614 + x2 = -72.42857143 + 120.2155614 Reorder the terms: 120.2155614 + -21.92857143x + x2 = -72.42857143 + 120.2155614 Combine like terms: -72.42857143 + 120.2155614 = 47.78698997 120.2155614 + -21.92857143x + x2 = 47.78698997 Factor a perfect square on the left side: (x + -10.96428572)(x + -10.96428572) = 47.78698997 Calculate the square root of the right side: 6.912813463 Break this problem into two subproblems by setting (x + -10.96428572) equal to 6.912813463 and -6.912813463.Subproblem 1
x + -10.96428572 = 6.912813463 Simplifying x + -10.96428572 = 6.912813463 Reorder the terms: -10.96428572 + x = 6.912813463 Solving -10.96428572 + x = 6.912813463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.96428572' to each side of the equation. -10.96428572 + 10.96428572 + x = 6.912813463 + 10.96428572 Combine like terms: -10.96428572 + 10.96428572 = 0.00000000 0.00000000 + x = 6.912813463 + 10.96428572 x = 6.912813463 + 10.96428572 Combine like terms: 6.912813463 + 10.96428572 = 17.877099183 x = 17.877099183 Simplifying x = 17.877099183Subproblem 2
x + -10.96428572 = -6.912813463 Simplifying x + -10.96428572 = -6.912813463 Reorder the terms: -10.96428572 + x = -6.912813463 Solving -10.96428572 + x = -6.912813463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.96428572' to each side of the equation. -10.96428572 + 10.96428572 + x = -6.912813463 + 10.96428572 Combine like terms: -10.96428572 + 10.96428572 = 0.00000000 0.00000000 + x = -6.912813463 + 10.96428572 x = -6.912813463 + 10.96428572 Combine like terms: -6.912813463 + 10.96428572 = 4.051472257 x = 4.051472257 Simplifying x = 4.051472257Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.877099183, 4.051472257}
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