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Simplifying 0 = 9x2 + -360x + 500 Reorder the terms: 0 = 500 + -360x + 9x2 Solving 0 = 500 + -360x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -500 = -500 -500 + 360x + -9x2 = 500 + -360x + 9x2 + -500 + 360x + -9x2 Reorder the terms: -500 + 360x + -9x2 = 500 + -500 + -360x + 360x + 9x2 + -9x2 Combine like terms: 500 + -500 = 0 -500 + 360x + -9x2 = 0 + -360x + 360x + 9x2 + -9x2 -500 + 360x + -9x2 = -360x + 360x + 9x2 + -9x2 Combine like terms: -360x + 360x = 0 -500 + 360x + -9x2 = 0 + 9x2 + -9x2 -500 + 360x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -500 + 360x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 55.55555556 + -40x + x2 = 0 Move the constant term to the right: Add '-55.55555556' to each side of the equation. 55.55555556 + -40x + -55.55555556 + x2 = 0 + -55.55555556 Reorder the terms: 55.55555556 + -55.55555556 + -40x + x2 = 0 + -55.55555556 Combine like terms: 55.55555556 + -55.55555556 = 0.00000000 0.00000000 + -40x + x2 = 0 + -55.55555556 -40x + x2 = 0 + -55.55555556 Combine like terms: 0 + -55.55555556 = -55.55555556 -40x + x2 = -55.55555556 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -55.55555556 + 400 Reorder the terms: 400 + -40x + x2 = -55.55555556 + 400 Combine like terms: -55.55555556 + 400 = 344.44444444 400 + -40x + x2 = 344.44444444 Factor a perfect square on the left side: (x + -20)(x + -20) = 344.44444444 Calculate the square root of the right side: 18.559214543 Break this problem into two subproblems by setting (x + -20) equal to 18.559214543 and -18.559214543.Subproblem 1
x + -20 = 18.559214543 Simplifying x + -20 = 18.559214543 Reorder the terms: -20 + x = 18.559214543 Solving -20 + x = 18.559214543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 18.559214543 + 20 Combine like terms: -20 + 20 = 0 0 + x = 18.559214543 + 20 x = 18.559214543 + 20 Combine like terms: 18.559214543 + 20 = 38.559214543 x = 38.559214543 Simplifying x = 38.559214543Subproblem 2
x + -20 = -18.559214543 Simplifying x + -20 = -18.559214543 Reorder the terms: -20 + x = -18.559214543 Solving -20 + x = -18.559214543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -18.559214543 + 20 Combine like terms: -20 + 20 = 0 0 + x = -18.559214543 + 20 x = -18.559214543 + 20 Combine like terms: -18.559214543 + 20 = 1.440785457 x = 1.440785457 Simplifying x = 1.440785457Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.559214543, 1.440785457}
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