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Simplifying 3x2 + 5x = 360 Reorder the terms: 5x + 3x2 = 360 Solving 5x + 3x2 = 360 Solving for variable 'x'. Reorder the terms: -360 + 5x + 3x2 = 360 + -360 Combine like terms: 360 + -360 = 0 -360 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -120 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + 1.666666667x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + 1.666666667x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + 1.666666667x + x2 = 0 + 120 1.666666667x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 1.666666667x + x2 = 120 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 120 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 120 + 0.6944444447 Combine like terms: 120 + 0.6944444447 = 120.6944444447 0.6944444447 + 1.666666667x + x2 = 120.6944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 120.6944444447 Calculate the square root of the right side: 10.986102332 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 10.986102332 and -10.986102332.Subproblem 1
x + 0.8333333335 = 10.986102332 Simplifying x + 0.8333333335 = 10.986102332 Reorder the terms: 0.8333333335 + x = 10.986102332 Solving 0.8333333335 + x = 10.986102332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 10.986102332 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 10.986102332 + -0.8333333335 x = 10.986102332 + -0.8333333335 Combine like terms: 10.986102332 + -0.8333333335 = 10.1527689985 x = 10.1527689985 Simplifying x = 10.1527689985Subproblem 2
x + 0.8333333335 = -10.986102332 Simplifying x + 0.8333333335 = -10.986102332 Reorder the terms: 0.8333333335 + x = -10.986102332 Solving 0.8333333335 + x = -10.986102332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -10.986102332 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -10.986102332 + -0.8333333335 x = -10.986102332 + -0.8333333335 Combine like terms: -10.986102332 + -0.8333333335 = -11.8194356655 x = -11.8194356655 Simplifying x = -11.8194356655Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.1527689985, -11.8194356655}
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