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Simplifying 6x(550 + -1x) + 4.50x = 3700 (550 * 6x + -1x * 6x) + 4.50x = 3700 (3300x + -6x2) + 4.50x = 3700 Reorder the terms: 3300x + 4.50x + -6x2 = 3700 Combine like terms: 3300x + 4.50x = 3304.5x 3304.5x + -6x2 = 3700 Solving 3304.5x + -6x2 = 3700 Solving for variable 'x'. Reorder the terms: -3700 + 3304.5x + -6x2 = 3700 + -3700 Combine like terms: 3700 + -3700 = 0 -3700 + 3304.5x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 616.6666667 + -550.75x + x2 = 0 Move the constant term to the right: Add '-616.6666667' to each side of the equation. 616.6666667 + -550.75x + -616.6666667 + x2 = 0 + -616.6666667 Reorder the terms: 616.6666667 + -616.6666667 + -550.75x + x2 = 0 + -616.6666667 Combine like terms: 616.6666667 + -616.6666667 = 0.0000000 0.0000000 + -550.75x + x2 = 0 + -616.6666667 -550.75x + x2 = 0 + -616.6666667 Combine like terms: 0 + -616.6666667 = -616.6666667 -550.75x + x2 = -616.6666667 The x term is -550.75x. Take half its coefficient (-275.375). Square it (75831.39063) and add it to both sides. Add '75831.39063' to each side of the equation. -550.75x + 75831.39063 + x2 = -616.6666667 + 75831.39063 Reorder the terms: 75831.39063 + -550.75x + x2 = -616.6666667 + 75831.39063 Combine like terms: -616.6666667 + 75831.39063 = 75214.7239633 75831.39063 + -550.75x + x2 = 75214.7239633 Factor a perfect square on the left side: (x + -275.375)(x + -275.375) = 75214.7239633 Calculate the square root of the right side: 274.253029087 Break this problem into two subproblems by setting (x + -275.375) equal to 274.253029087 and -274.253029087.Subproblem 1
x + -275.375 = 274.253029087 Simplifying x + -275.375 = 274.253029087 Reorder the terms: -275.375 + x = 274.253029087 Solving -275.375 + x = 274.253029087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '275.375' to each side of the equation. -275.375 + 275.375 + x = 274.253029087 + 275.375 Combine like terms: -275.375 + 275.375 = 0.000 0.000 + x = 274.253029087 + 275.375 x = 274.253029087 + 275.375 Combine like terms: 274.253029087 + 275.375 = 549.628029087 x = 549.628029087 Simplifying x = 549.628029087Subproblem 2
x + -275.375 = -274.253029087 Simplifying x + -275.375 = -274.253029087 Reorder the terms: -275.375 + x = -274.253029087 Solving -275.375 + x = -274.253029087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '275.375' to each side of the equation. -275.375 + 275.375 + x = -274.253029087 + 275.375 Combine like terms: -275.375 + 275.375 = 0.000 0.000 + x = -274.253029087 + 275.375 x = -274.253029087 + 275.375 Combine like terms: -274.253029087 + 275.375 = 1.121970913 x = 1.121970913 Simplifying x = 1.121970913Solution
The solution to the problem is based on the solutions from the subproblems. x = {549.628029087, 1.121970913}
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