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Simplifying 0.071x2 + 1.071x + -154 = 0 Reorder the terms: -154 + 1.071x + 0.071x2 = 0 Solving -154 + 1.071x + 0.071x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.071 the coefficient of the squared term: Divide each side by '0.071'. -2169.014085 + 15.08450704x + x2 = 0 Move the constant term to the right: Add '2169.014085' to each side of the equation. -2169.014085 + 15.08450704x + 2169.014085 + x2 = 0 + 2169.014085 Reorder the terms: -2169.014085 + 2169.014085 + 15.08450704x + x2 = 0 + 2169.014085 Combine like terms: -2169.014085 + 2169.014085 = 0.000000 0.000000 + 15.08450704x + x2 = 0 + 2169.014085 15.08450704x + x2 = 0 + 2169.014085 Combine like terms: 0 + 2169.014085 = 2169.014085 15.08450704x + x2 = 2169.014085 The x term is 15.08450704x. Take half its coefficient (7.54225352). Square it (56.88558816) and add it to both sides. Add '56.88558816' to each side of the equation. 15.08450704x + 56.88558816 + x2 = 2169.014085 + 56.88558816 Reorder the terms: 56.88558816 + 15.08450704x + x2 = 2169.014085 + 56.88558816 Combine like terms: 2169.014085 + 56.88558816 = 2225.89967316 56.88558816 + 15.08450704x + x2 = 2225.89967316 Factor a perfect square on the left side: (x + 7.54225352)(x + 7.54225352) = 2225.89967316 Calculate the square root of the right side: 47.179441213 Break this problem into two subproblems by setting (x + 7.54225352) equal to 47.179441213 and -47.179441213.Subproblem 1
x + 7.54225352 = 47.179441213 Simplifying x + 7.54225352 = 47.179441213 Reorder the terms: 7.54225352 + x = 47.179441213 Solving 7.54225352 + x = 47.179441213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.54225352' to each side of the equation. 7.54225352 + -7.54225352 + x = 47.179441213 + -7.54225352 Combine like terms: 7.54225352 + -7.54225352 = 0.00000000 0.00000000 + x = 47.179441213 + -7.54225352 x = 47.179441213 + -7.54225352 Combine like terms: 47.179441213 + -7.54225352 = 39.637187693 x = 39.637187693 Simplifying x = 39.637187693Subproblem 2
x + 7.54225352 = -47.179441213 Simplifying x + 7.54225352 = -47.179441213 Reorder the terms: 7.54225352 + x = -47.179441213 Solving 7.54225352 + x = -47.179441213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.54225352' to each side of the equation. 7.54225352 + -7.54225352 + x = -47.179441213 + -7.54225352 Combine like terms: 7.54225352 + -7.54225352 = 0.00000000 0.00000000 + x = -47.179441213 + -7.54225352 x = -47.179441213 + -7.54225352 Combine like terms: -47.179441213 + -7.54225352 = -54.721694733 x = -54.721694733 Simplifying x = -54.721694733Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.637187693, -54.721694733}
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