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Simplifying (2x + -7)(4x + 10) = 9 Reorder the terms: (-7 + 2x)(4x + 10) = 9 Reorder the terms: (-7 + 2x)(10 + 4x) = 9 Multiply (-7 + 2x) * (10 + 4x) (-7(10 + 4x) + 2x * (10 + 4x)) = 9 ((10 * -7 + 4x * -7) + 2x * (10 + 4x)) = 9 ((-70 + -28x) + 2x * (10 + 4x)) = 9 (-70 + -28x + (10 * 2x + 4x * 2x)) = 9 (-70 + -28x + (20x + 8x2)) = 9 Combine like terms: -28x + 20x = -8x (-70 + -8x + 8x2) = 9 Solving -70 + -8x + 8x2 = 9 Solving for variable 'x'. Reorder the terms: -70 + -9 + -8x + 8x2 = 9 + -9 Combine like terms: -70 + -9 = -79 -79 + -8x + 8x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -79 + -8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -9.875 + -1x + x2 = 0 Move the constant term to the right: Add '9.875' to each side of the equation. -9.875 + -1x + 9.875 + x2 = 0 + 9.875 Reorder the terms: -9.875 + 9.875 + -1x + x2 = 0 + 9.875 Combine like terms: -9.875 + 9.875 = 0.000 0.000 + -1x + x2 = 0 + 9.875 -1x + x2 = 0 + 9.875 Combine like terms: 0 + 9.875 = 9.875 -1x + x2 = 9.875 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 9.875 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 9.875 + 0.25 Combine like terms: 9.875 + 0.25 = 10.125 0.25 + -1x + x2 = 10.125 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 10.125 Calculate the square root of the right side: 3.181980515 Break this problem into two subproblems by setting (x + -0.5) equal to 3.181980515 and -3.181980515.Subproblem 1
x + -0.5 = 3.181980515 Simplifying x + -0.5 = 3.181980515 Reorder the terms: -0.5 + x = 3.181980515 Solving -0.5 + x = 3.181980515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.181980515 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.181980515 + 0.5 x = 3.181980515 + 0.5 Combine like terms: 3.181980515 + 0.5 = 3.681980515 x = 3.681980515 Simplifying x = 3.681980515Subproblem 2
x + -0.5 = -3.181980515 Simplifying x + -0.5 = -3.181980515 Reorder the terms: -0.5 + x = -3.181980515 Solving -0.5 + x = -3.181980515 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.181980515 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.181980515 + 0.5 x = -3.181980515 + 0.5 Combine like terms: -3.181980515 + 0.5 = -2.681980515 x = -2.681980515 Simplifying x = -2.681980515Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.681980515, -2.681980515}
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