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Simplifying 4x2 + -9x = 74 Reorder the terms: -9x + 4x2 = 74 Solving -9x + 4x2 = 74 Solving for variable 'x'. Reorder the terms: -74 + -9x + 4x2 = 74 + -74 Combine like terms: 74 + -74 = 0 -74 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18.5 + -2.25x + x2 = 0 Move the constant term to the right: Add '18.5' to each side of the equation. -18.5 + -2.25x + 18.5 + x2 = 0 + 18.5 Reorder the terms: -18.5 + 18.5 + -2.25x + x2 = 0 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + -2.25x + x2 = 0 + 18.5 -2.25x + x2 = 0 + 18.5 Combine like terms: 0 + 18.5 = 18.5 -2.25x + x2 = 18.5 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 18.5 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 18.5 + 1.265625 Combine like terms: 18.5 + 1.265625 = 19.765625 1.265625 + -2.25x + x2 = 19.765625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 19.765625 Calculate the square root of the right side: 4.445854811 Break this problem into two subproblems by setting (x + -1.125) equal to 4.445854811 and -4.445854811.Subproblem 1
x + -1.125 = 4.445854811 Simplifying x + -1.125 = 4.445854811 Reorder the terms: -1.125 + x = 4.445854811 Solving -1.125 + x = 4.445854811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 4.445854811 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 4.445854811 + 1.125 x = 4.445854811 + 1.125 Combine like terms: 4.445854811 + 1.125 = 5.570854811 x = 5.570854811 Simplifying x = 5.570854811Subproblem 2
x + -1.125 = -4.445854811 Simplifying x + -1.125 = -4.445854811 Reorder the terms: -1.125 + x = -4.445854811 Solving -1.125 + x = -4.445854811 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -4.445854811 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -4.445854811 + 1.125 x = -4.445854811 + 1.125 Combine like terms: -4.445854811 + 1.125 = -3.320854811 x = -3.320854811 Simplifying x = -3.320854811Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.570854811, -3.320854811}
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