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Simplifying 4x2 + -22x + -17x = 65.45 + -11 * 8.5 Reorder the terms: -22x + -17x + 4x2 = 65.45 + -11 * 8.5 Combine like terms: -22x + -17x = -39x -39x + 4x2 = 65.45 + -11 * 8.5 Multiply -11 * 8.5 -39x + 4x2 = 65.45 + -93.5 Combine like terms: 65.45 + -93.5 = -28.05 -39x + 4x2 = -28.05 Solving -39x + 4x2 = -28.05 Solving for variable 'x'. Reorder the terms: 28.05 + -39x + 4x2 = -28.05 + 28.05 Combine like terms: -28.05 + 28.05 = 0.00 28.05 + -39x + 4x2 = 0.00 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7.0125 + -9.75x + x2 = 0.00 Move the constant term to the right: Add '-7.0125' to each side of the equation. 7.0125 + -9.75x + -7.0125 + x2 = 0.00 + -7.0125 Reorder the terms: 7.0125 + -7.0125 + -9.75x + x2 = 0.00 + -7.0125 Combine like terms: 7.0125 + -7.0125 = 0.0000 0.0000 + -9.75x + x2 = 0.00 + -7.0125 -9.75x + x2 = 0.00 + -7.0125 Combine like terms: 0.00 + -7.0125 = -7.0125 -9.75x + x2 = -7.0125 The x term is -9.75x. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75x + 23.765625 + x2 = -7.0125 + 23.765625 Reorder the terms: 23.765625 + -9.75x + x2 = -7.0125 + 23.765625 Combine like terms: -7.0125 + 23.765625 = 16.753125 23.765625 + -9.75x + x2 = 16.753125 Factor a perfect square on the left side: (x + -4.875)(x + -4.875) = 16.753125 Calculate the square root of the right side: 4.093058148 Break this problem into two subproblems by setting (x + -4.875) equal to 4.093058148 and -4.093058148.Subproblem 1
x + -4.875 = 4.093058148 Simplifying x + -4.875 = 4.093058148 Reorder the terms: -4.875 + x = 4.093058148 Solving -4.875 + x = 4.093058148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = 4.093058148 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = 4.093058148 + 4.875 x = 4.093058148 + 4.875 Combine like terms: 4.093058148 + 4.875 = 8.968058148 x = 8.968058148 Simplifying x = 8.968058148Subproblem 2
x + -4.875 = -4.093058148 Simplifying x + -4.875 = -4.093058148 Reorder the terms: -4.875 + x = -4.093058148 Solving -4.875 + x = -4.093058148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = -4.093058148 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = -4.093058148 + 4.875 x = -4.093058148 + 4.875 Combine like terms: -4.093058148 + 4.875 = 0.781941852 x = 0.781941852 Simplifying x = 0.781941852Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.968058148, 0.781941852}
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