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Simplifying 12x2 + -202.8x + 623.7 = 0 Reorder the terms: 623.7 + -202.8x + 12x2 = 0 Solving 623.7 + -202.8x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 51.975 + -16.9x + x2 = 0 Move the constant term to the right: Add '-51.975' to each side of the equation. 51.975 + -16.9x + -51.975 + x2 = 0 + -51.975 Reorder the terms: 51.975 + -51.975 + -16.9x + x2 = 0 + -51.975 Combine like terms: 51.975 + -51.975 = 0.000 0.000 + -16.9x + x2 = 0 + -51.975 -16.9x + x2 = 0 + -51.975 Combine like terms: 0 + -51.975 = -51.975 -16.9x + x2 = -51.975 The x term is -16.9x. Take half its coefficient (-8.45). Square it (71.4025) and add it to both sides. Add '71.4025' to each side of the equation. -16.9x + 71.4025 + x2 = -51.975 + 71.4025 Reorder the terms: 71.4025 + -16.9x + x2 = -51.975 + 71.4025 Combine like terms: -51.975 + 71.4025 = 19.4275 71.4025 + -16.9x + x2 = 19.4275 Factor a perfect square on the left side: (x + -8.45)(x + -8.45) = 19.4275 Calculate the square root of the right side: 4.40766378 Break this problem into two subproblems by setting (x + -8.45) equal to 4.40766378 and -4.40766378.Subproblem 1
x + -8.45 = 4.40766378 Simplifying x + -8.45 = 4.40766378 Reorder the terms: -8.45 + x = 4.40766378 Solving -8.45 + x = 4.40766378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.45' to each side of the equation. -8.45 + 8.45 + x = 4.40766378 + 8.45 Combine like terms: -8.45 + 8.45 = 0.00 0.00 + x = 4.40766378 + 8.45 x = 4.40766378 + 8.45 Combine like terms: 4.40766378 + 8.45 = 12.85766378 x = 12.85766378 Simplifying x = 12.85766378Subproblem 2
x + -8.45 = -4.40766378 Simplifying x + -8.45 = -4.40766378 Reorder the terms: -8.45 + x = -4.40766378 Solving -8.45 + x = -4.40766378 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.45' to each side of the equation. -8.45 + 8.45 + x = -4.40766378 + 8.45 Combine like terms: -8.45 + 8.45 = 0.00 0.00 + x = -4.40766378 + 8.45 x = -4.40766378 + 8.45 Combine like terms: -4.40766378 + 8.45 = 4.04233622 x = 4.04233622 Simplifying x = 4.04233622Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.85766378, 4.04233622}
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