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Simplifying (4x + -7)(x + -9) = 6x Reorder the terms: (-7 + 4x)(x + -9) = 6x Reorder the terms: (-7 + 4x)(-9 + x) = 6x Multiply (-7 + 4x) * (-9 + x) (-7(-9 + x) + 4x * (-9 + x)) = 6x ((-9 * -7 + x * -7) + 4x * (-9 + x)) = 6x ((63 + -7x) + 4x * (-9 + x)) = 6x (63 + -7x + (-9 * 4x + x * 4x)) = 6x (63 + -7x + (-36x + 4x2)) = 6x Combine like terms: -7x + -36x = -43x (63 + -43x + 4x2) = 6x Solving 63 + -43x + 4x2 = 6x Solving for variable 'x'. Reorder the terms: 63 + -43x + -6x + 4x2 = 6x + -6x Combine like terms: -43x + -6x = -49x 63 + -49x + 4x2 = 6x + -6x Combine like terms: 6x + -6x = 0 63 + -49x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 15.75 + -12.25x + x2 = 0 Move the constant term to the right: Add '-15.75' to each side of the equation. 15.75 + -12.25x + -15.75 + x2 = 0 + -15.75 Reorder the terms: 15.75 + -15.75 + -12.25x + x2 = 0 + -15.75 Combine like terms: 15.75 + -15.75 = 0.00 0.00 + -12.25x + x2 = 0 + -15.75 -12.25x + x2 = 0 + -15.75 Combine like terms: 0 + -15.75 = -15.75 -12.25x + x2 = -15.75 The x term is -12.25x. Take half its coefficient (-6.125). Square it (37.515625) and add it to both sides. Add '37.515625' to each side of the equation. -12.25x + 37.515625 + x2 = -15.75 + 37.515625 Reorder the terms: 37.515625 + -12.25x + x2 = -15.75 + 37.515625 Combine like terms: -15.75 + 37.515625 = 21.765625 37.515625 + -12.25x + x2 = 21.765625 Factor a perfect square on the left side: (x + -6.125)(x + -6.125) = 21.765625 Calculate the square root of the right side: 4.665364402 Break this problem into two subproblems by setting (x + -6.125) equal to 4.665364402 and -4.665364402.Subproblem 1
x + -6.125 = 4.665364402 Simplifying x + -6.125 = 4.665364402 Reorder the terms: -6.125 + x = 4.665364402 Solving -6.125 + x = 4.665364402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = 4.665364402 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = 4.665364402 + 6.125 x = 4.665364402 + 6.125 Combine like terms: 4.665364402 + 6.125 = 10.790364402 x = 10.790364402 Simplifying x = 10.790364402Subproblem 2
x + -6.125 = -4.665364402 Simplifying x + -6.125 = -4.665364402 Reorder the terms: -6.125 + x = -4.665364402 Solving -6.125 + x = -4.665364402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.125' to each side of the equation. -6.125 + 6.125 + x = -4.665364402 + 6.125 Combine like terms: -6.125 + 6.125 = 0.000 0.000 + x = -4.665364402 + 6.125 x = -4.665364402 + 6.125 Combine like terms: -4.665364402 + 6.125 = 1.459635598 x = 1.459635598 Simplifying x = 1.459635598Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.790364402, 1.459635598}
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