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Simplifying (7 + -1x)(3 + 4x) = 9 Multiply (7 + -1x) * (3 + 4x) (7(3 + 4x) + -1x * (3 + 4x)) = 9 ((3 * 7 + 4x * 7) + -1x * (3 + 4x)) = 9 ((21 + 28x) + -1x * (3 + 4x)) = 9 (21 + 28x + (3 * -1x + 4x * -1x)) = 9 (21 + 28x + (-3x + -4x2)) = 9 Combine like terms: 28x + -3x = 25x (21 + 25x + -4x2) = 9 Solving 21 + 25x + -4x2 = 9 Solving for variable 'x'. Reorder the terms: 21 + -9 + 25x + -4x2 = 9 + -9 Combine like terms: 21 + -9 = 12 12 + 25x + -4x2 = 9 + -9 Combine like terms: 9 + -9 = 0 12 + 25x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3 + -6.25x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -6.25x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -6.25x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6.25x + x2 = 0 + 3 -6.25x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6.25x + x2 = 3 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 3 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 3 + 9.765625 Combine like terms: 3 + 9.765625 = 12.765625 9.765625 + -6.25x + x2 = 12.765625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 12.765625 Calculate the square root of the right side: 3.572901482 Break this problem into two subproblems by setting (x + -3.125) equal to 3.572901482 and -3.572901482.Subproblem 1
x + -3.125 = 3.572901482 Simplifying x + -3.125 = 3.572901482 Reorder the terms: -3.125 + x = 3.572901482 Solving -3.125 + x = 3.572901482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 3.572901482 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 3.572901482 + 3.125 x = 3.572901482 + 3.125 Combine like terms: 3.572901482 + 3.125 = 6.697901482 x = 6.697901482 Simplifying x = 6.697901482Subproblem 2
x + -3.125 = -3.572901482 Simplifying x + -3.125 = -3.572901482 Reorder the terms: -3.125 + x = -3.572901482 Solving -3.125 + x = -3.572901482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -3.572901482 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -3.572901482 + 3.125 x = -3.572901482 + 3.125 Combine like terms: -3.572901482 + 3.125 = -0.447901482 x = -0.447901482 Simplifying x = -0.447901482Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.697901482, -0.447901482}
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