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Simplifying -0.08x2 + 2.88x = 14 Reorder the terms: 2.88x + -0.08x2 = 14 Solving 2.88x + -0.08x2 = 14 Solving for variable 'x'. Reorder the terms: -14 + 2.88x + -0.08x2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 2.88x + -0.08x2 = 0 Begin completing the square. Divide all terms by -0.08 the coefficient of the squared term: Divide each side by '-0.08'. 175 + -36x + x2 = 0 Move the constant term to the right: Add '-175' to each side of the equation. 175 + -36x + -175 + x2 = 0 + -175 Reorder the terms: 175 + -175 + -36x + x2 = 0 + -175 Combine like terms: 175 + -175 = 0 0 + -36x + x2 = 0 + -175 -36x + x2 = 0 + -175 Combine like terms: 0 + -175 = -175 -36x + x2 = -175 The x term is -36x. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36x + 324 + x2 = -175 + 324 Reorder the terms: 324 + -36x + x2 = -175 + 324 Combine like terms: -175 + 324 = 149 324 + -36x + x2 = 149 Factor a perfect square on the left side: (x + -18)(x + -18) = 149 Calculate the square root of the right side: 12.206555616 Break this problem into two subproblems by setting (x + -18) equal to 12.206555616 and -12.206555616.Subproblem 1
x + -18 = 12.206555616 Simplifying x + -18 = 12.206555616 Reorder the terms: -18 + x = 12.206555616 Solving -18 + x = 12.206555616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = 12.206555616 + 18 Combine like terms: -18 + 18 = 0 0 + x = 12.206555616 + 18 x = 12.206555616 + 18 Combine like terms: 12.206555616 + 18 = 30.206555616 x = 30.206555616 Simplifying x = 30.206555616Subproblem 2
x + -18 = -12.206555616 Simplifying x + -18 = -12.206555616 Reorder the terms: -18 + x = -12.206555616 Solving -18 + x = -12.206555616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + x = -12.206555616 + 18 Combine like terms: -18 + 18 = 0 0 + x = -12.206555616 + 18 x = -12.206555616 + 18 Combine like terms: -12.206555616 + 18 = 5.793444384 x = 5.793444384 Simplifying x = 5.793444384Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.206555616, 5.793444384}
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