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Simplifying -0.08x2 + 2.88x = 6 Reorder the terms: 2.88x + -0.08x2 = 6 Solving 2.88x + -0.08x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + 2.88x + -0.08x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + 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'. 75 + -36x + x2 = 0 Move the constant term to the right: Add '-75' to each side of the equation. 75 + -36x + -75 + x2 = 0 + -75 Reorder the terms: 75 + -75 + -36x + x2 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -36x + x2 = 0 + -75 -36x + x2 = 0 + -75 Combine like terms: 0 + -75 = -75 -36x + x2 = -75 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 = -75 + 324 Reorder the terms: 324 + -36x + x2 = -75 + 324 Combine like terms: -75 + 324 = 249 324 + -36x + x2 = 249 Factor a perfect square on the left side: (x + -18)(x + -18) = 249 Calculate the square root of the right side: 15.779733838 Break this problem into two subproblems by setting (x + -18) equal to 15.779733838 and -15.779733838.Subproblem 1
x + -18 = 15.779733838 Simplifying x + -18 = 15.779733838 Reorder the terms: -18 + x = 15.779733838 Solving -18 + x = 15.779733838 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 = 15.779733838 + 18 Combine like terms: -18 + 18 = 0 0 + x = 15.779733838 + 18 x = 15.779733838 + 18 Combine like terms: 15.779733838 + 18 = 33.779733838 x = 33.779733838 Simplifying x = 33.779733838Subproblem 2
x + -18 = -15.779733838 Simplifying x + -18 = -15.779733838 Reorder the terms: -18 + x = -15.779733838 Solving -18 + x = -15.779733838 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 = -15.779733838 + 18 Combine like terms: -18 + 18 = 0 0 + x = -15.779733838 + 18 x = -15.779733838 + 18 Combine like terms: -15.779733838 + 18 = 2.220266162 x = 2.220266162 Simplifying x = 2.220266162Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.779733838, 2.220266162}
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