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Simplifying (2x + 11)(3x + -7) = 87 Reorder the terms: (11 + 2x)(3x + -7) = 87 Reorder the terms: (11 + 2x)(-7 + 3x) = 87 Multiply (11 + 2x) * (-7 + 3x) (11(-7 + 3x) + 2x * (-7 + 3x)) = 87 ((-7 * 11 + 3x * 11) + 2x * (-7 + 3x)) = 87 ((-77 + 33x) + 2x * (-7 + 3x)) = 87 (-77 + 33x + (-7 * 2x + 3x * 2x)) = 87 (-77 + 33x + (-14x + 6x2)) = 87 Combine like terms: 33x + -14x = 19x (-77 + 19x + 6x2) = 87 Solving -77 + 19x + 6x2 = 87 Solving for variable 'x'. Reorder the terms: -77 + -87 + 19x + 6x2 = 87 + -87 Combine like terms: -77 + -87 = -164 -164 + 19x + 6x2 = 87 + -87 Combine like terms: 87 + -87 = 0 -164 + 19x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -27.33333333 + 3.166666667x + x2 = 0 Move the constant term to the right: Add '27.33333333' to each side of the equation. -27.33333333 + 3.166666667x + 27.33333333 + x2 = 0 + 27.33333333 Reorder the terms: -27.33333333 + 27.33333333 + 3.166666667x + x2 = 0 + 27.33333333 Combine like terms: -27.33333333 + 27.33333333 = 0.00000000 0.00000000 + 3.166666667x + x2 = 0 + 27.33333333 3.166666667x + x2 = 0 + 27.33333333 Combine like terms: 0 + 27.33333333 = 27.33333333 3.166666667x + x2 = 27.33333333 The x term is 3.166666667x. Take half its coefficient (1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. 3.166666667x + 2.506944447 + x2 = 27.33333333 + 2.506944447 Reorder the terms: 2.506944447 + 3.166666667x + x2 = 27.33333333 + 2.506944447 Combine like terms: 27.33333333 + 2.506944447 = 29.840277777 2.506944447 + 3.166666667x + x2 = 29.840277777 Factor a perfect square on the left side: (x + 1.583333334)(x + 1.583333334) = 29.840277777 Calculate the square root of the right side: 5.462625539 Break this problem into two subproblems by setting (x + 1.583333334) equal to 5.462625539 and -5.462625539.Subproblem 1
x + 1.583333334 = 5.462625539 Simplifying x + 1.583333334 = 5.462625539 Reorder the terms: 1.583333334 + x = 5.462625539 Solving 1.583333334 + x = 5.462625539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.583333334' to each side of the equation. 1.583333334 + -1.583333334 + x = 5.462625539 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = 5.462625539 + -1.583333334 x = 5.462625539 + -1.583333334 Combine like terms: 5.462625539 + -1.583333334 = 3.879292205 x = 3.879292205 Simplifying x = 3.879292205Subproblem 2
x + 1.583333334 = -5.462625539 Simplifying x + 1.583333334 = -5.462625539 Reorder the terms: 1.583333334 + x = -5.462625539 Solving 1.583333334 + x = -5.462625539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.583333334' to each side of the equation. 1.583333334 + -1.583333334 + x = -5.462625539 + -1.583333334 Combine like terms: 1.583333334 + -1.583333334 = 0.000000000 0.000000000 + x = -5.462625539 + -1.583333334 x = -5.462625539 + -1.583333334 Combine like terms: -5.462625539 + -1.583333334 = -7.045958873 x = -7.045958873 Simplifying x = -7.045958873Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.879292205, -7.045958873}
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