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Simplifying 720 = -0.5x2 + 50x + -472 Reorder the terms: 720 = -472 + 50x + -0.5x2 Solving 720 = -472 + 50x + -0.5x2 Solving for variable 'x'. Combine like terms: 720 + 472 = 1192 1192 + -50x + 0.5x2 = -472 + 50x + -0.5x2 + 472 + -50x + 0.5x2 Reorder the terms: 1192 + -50x + 0.5x2 = -472 + 472 + 50x + -50x + -0.5x2 + 0.5x2 Combine like terms: -472 + 472 = 0 1192 + -50x + 0.5x2 = 0 + 50x + -50x + -0.5x2 + 0.5x2 1192 + -50x + 0.5x2 = 50x + -50x + -0.5x2 + 0.5x2 Combine like terms: 50x + -50x = 0 1192 + -50x + 0.5x2 = 0 + -0.5x2 + 0.5x2 1192 + -50x + 0.5x2 = -0.5x2 + 0.5x2 Combine like terms: -0.5x2 + 0.5x2 = 0.0 1192 + -50x + 0.5x2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 2384 + -100x + x2 = 0 Move the constant term to the right: Add '-2384' to each side of the equation. 2384 + -100x + -2384 + x2 = 0 + -2384 Reorder the terms: 2384 + -2384 + -100x + x2 = 0 + -2384 Combine like terms: 2384 + -2384 = 0 0 + -100x + x2 = 0 + -2384 -100x + x2 = 0 + -2384 Combine like terms: 0 + -2384 = -2384 -100x + x2 = -2384 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -2384 + 2500 Reorder the terms: 2500 + -100x + x2 = -2384 + 2500 Combine like terms: -2384 + 2500 = 116 2500 + -100x + x2 = 116 Factor a perfect square on the left side: (x + -50)(x + -50) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (x + -50) equal to 10.770329614 and -10.770329614.Subproblem 1
x + -50 = 10.770329614 Simplifying x + -50 = 10.770329614 Reorder the terms: -50 + x = 10.770329614 Solving -50 + x = 10.770329614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 10.770329614 + 50 Combine like terms: -50 + 50 = 0 0 + x = 10.770329614 + 50 x = 10.770329614 + 50 Combine like terms: 10.770329614 + 50 = 60.770329614 x = 60.770329614 Simplifying x = 60.770329614Subproblem 2
x + -50 = -10.770329614 Simplifying x + -50 = -10.770329614 Reorder the terms: -50 + x = -10.770329614 Solving -50 + x = -10.770329614 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -10.770329614 + 50 Combine like terms: -50 + 50 = 0 0 + x = -10.770329614 + 50 x = -10.770329614 + 50 Combine like terms: -10.770329614 + 50 = 39.229670386 x = 39.229670386 Simplifying x = 39.229670386Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.770329614, 39.229670386}
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