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Simplifying (2x + 9)(4x + -7) = 38 Reorder the terms: (9 + 2x)(4x + -7) = 38 Reorder the terms: (9 + 2x)(-7 + 4x) = 38 Multiply (9 + 2x) * (-7 + 4x) (9(-7 + 4x) + 2x * (-7 + 4x)) = 38 ((-7 * 9 + 4x * 9) + 2x * (-7 + 4x)) = 38 ((-63 + 36x) + 2x * (-7 + 4x)) = 38 (-63 + 36x + (-7 * 2x + 4x * 2x)) = 38 (-63 + 36x + (-14x + 8x2)) = 38 Combine like terms: 36x + -14x = 22x (-63 + 22x + 8x2) = 38 Solving -63 + 22x + 8x2 = 38 Solving for variable 'x'. Reorder the terms: -63 + -38 + 22x + 8x2 = 38 + -38 Combine like terms: -63 + -38 = -101 -101 + 22x + 8x2 = 38 + -38 Combine like terms: 38 + -38 = 0 -101 + 22x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -12.625 + 2.75x + x2 = 0 Move the constant term to the right: Add '12.625' to each side of the equation. -12.625 + 2.75x + 12.625 + x2 = 0 + 12.625 Reorder the terms: -12.625 + 12.625 + 2.75x + x2 = 0 + 12.625 Combine like terms: -12.625 + 12.625 = 0.000 0.000 + 2.75x + x2 = 0 + 12.625 2.75x + x2 = 0 + 12.625 Combine like terms: 0 + 12.625 = 12.625 2.75x + x2 = 12.625 The x term is 2.75x. Take half its coefficient (1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. 2.75x + 1.890625 + x2 = 12.625 + 1.890625 Reorder the terms: 1.890625 + 2.75x + x2 = 12.625 + 1.890625 Combine like terms: 12.625 + 1.890625 = 14.515625 1.890625 + 2.75x + x2 = 14.515625 Factor a perfect square on the left side: (x + 1.375)(x + 1.375) = 14.515625 Calculate the square root of the right side: 3.809937664 Break this problem into two subproblems by setting (x + 1.375) equal to 3.809937664 and -3.809937664.Subproblem 1
x + 1.375 = 3.809937664 Simplifying x + 1.375 = 3.809937664 Reorder the terms: 1.375 + x = 3.809937664 Solving 1.375 + x = 3.809937664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = 3.809937664 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = 3.809937664 + -1.375 x = 3.809937664 + -1.375 Combine like terms: 3.809937664 + -1.375 = 2.434937664 x = 2.434937664 Simplifying x = 2.434937664Subproblem 2
x + 1.375 = -3.809937664 Simplifying x + 1.375 = -3.809937664 Reorder the terms: 1.375 + x = -3.809937664 Solving 1.375 + x = -3.809937664 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.375' to each side of the equation. 1.375 + -1.375 + x = -3.809937664 + -1.375 Combine like terms: 1.375 + -1.375 = 0.000 0.000 + x = -3.809937664 + -1.375 x = -3.809937664 + -1.375 Combine like terms: -3.809937664 + -1.375 = -5.184937664 x = -5.184937664 Simplifying x = -5.184937664Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.434937664, -5.184937664}
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