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Simplifying 50.5(x2 + -3x + 2) = 4x2 Reorder the terms: 50.5(2 + -3x + x2) = 4x2 (2 * 50.5 + -3x * 50.5 + x2 * 50.5) = 4x2 (101 + -151.5x + 50.5x2) = 4x2 Solving 101 + -151.5x + 50.5x2 = 4x2 Solving for variable 'x'. Combine like terms: 50.5x2 + -4x2 = 46.5x2 101 + -151.5x + 46.5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 101 + -151.5x + 46.5x2 = 0 Begin completing the square. Divide all terms by 46.5 the coefficient of the squared term: Divide each side by '46.5'. 2.172043011 + -3.258064516x + x2 = 0 Move the constant term to the right: Add '-2.172043011' to each side of the equation. 2.172043011 + -3.258064516x + -2.172043011 + x2 = 0 + -2.172043011 Reorder the terms: 2.172043011 + -2.172043011 + -3.258064516x + x2 = 0 + -2.172043011 Combine like terms: 2.172043011 + -2.172043011 = 0.000000000 0.000000000 + -3.258064516x + x2 = 0 + -2.172043011 -3.258064516x + x2 = 0 + -2.172043011 Combine like terms: 0 + -2.172043011 = -2.172043011 -3.258064516x + x2 = -2.172043011 The x term is -3.258064516x. Take half its coefficient (-1.629032258). Square it (2.653746098) and add it to both sides. Add '2.653746098' to each side of the equation. -3.258064516x + 2.653746098 + x2 = -2.172043011 + 2.653746098 Reorder the terms: 2.653746098 + -3.258064516x + x2 = -2.172043011 + 2.653746098 Combine like terms: -2.172043011 + 2.653746098 = 0.481703087 2.653746098 + -3.258064516x + x2 = 0.481703087 Factor a perfect square on the left side: (x + -1.629032258)(x + -1.629032258) = 0.481703087 Calculate the square root of the right side: 0.694048332 Break this problem into two subproblems by setting (x + -1.629032258) equal to 0.694048332 and -0.694048332.Subproblem 1
x + -1.629032258 = 0.694048332 Simplifying x + -1.629032258 = 0.694048332 Reorder the terms: -1.629032258 + x = 0.694048332 Solving -1.629032258 + x = 0.694048332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.629032258' to each side of the equation. -1.629032258 + 1.629032258 + x = 0.694048332 + 1.629032258 Combine like terms: -1.629032258 + 1.629032258 = 0.000000000 0.000000000 + x = 0.694048332 + 1.629032258 x = 0.694048332 + 1.629032258 Combine like terms: 0.694048332 + 1.629032258 = 2.32308059 x = 2.32308059 Simplifying x = 2.32308059Subproblem 2
x + -1.629032258 = -0.694048332 Simplifying x + -1.629032258 = -0.694048332 Reorder the terms: -1.629032258 + x = -0.694048332 Solving -1.629032258 + x = -0.694048332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.629032258' to each side of the equation. -1.629032258 + 1.629032258 + x = -0.694048332 + 1.629032258 Combine like terms: -1.629032258 + 1.629032258 = 0.000000000 0.000000000 + x = -0.694048332 + 1.629032258 x = -0.694048332 + 1.629032258 Combine like terms: -0.694048332 + 1.629032258 = 0.934983926 x = 0.934983926 Simplifying x = 0.934983926Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.32308059, 0.934983926}
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