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Simplifying (3x + 7)(x + -7) = -16 Reorder the terms: (7 + 3x)(x + -7) = -16 Reorder the terms: (7 + 3x)(-7 + x) = -16 Multiply (7 + 3x) * (-7 + x) (7(-7 + x) + 3x * (-7 + x)) = -16 ((-7 * 7 + x * 7) + 3x * (-7 + x)) = -16 ((-49 + 7x) + 3x * (-7 + x)) = -16 (-49 + 7x + (-7 * 3x + x * 3x)) = -16 (-49 + 7x + (-21x + 3x2)) = -16 Combine like terms: 7x + -21x = -14x (-49 + -14x + 3x2) = -16 Solving -49 + -14x + 3x2 = -16 Solving for variable 'x'. Reorder the terms: -49 + 16 + -14x + 3x2 = -16 + 16 Combine like terms: -49 + 16 = -33 -33 + -14x + 3x2 = -16 + 16 Combine like terms: -16 + 16 = 0 -33 + -14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -4.666666667x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -4.666666667x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -4.666666667x + x2 = 0 + 11 -4.666666667x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -4.666666667x + x2 = 11 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = 11 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = 11 + 5.444444448 Combine like terms: 11 + 5.444444448 = 16.444444448 5.444444448 + -4.666666667x + x2 = 16.444444448 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = 16.444444448 Calculate the square root of the right side: 4.055175021 Break this problem into two subproblems by setting (x + -2.333333334) equal to 4.055175021 and -4.055175021.Subproblem 1
x + -2.333333334 = 4.055175021 Simplifying x + -2.333333334 = 4.055175021 Reorder the terms: -2.333333334 + x = 4.055175021 Solving -2.333333334 + x = 4.055175021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = 4.055175021 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = 4.055175021 + 2.333333334 x = 4.055175021 + 2.333333334 Combine like terms: 4.055175021 + 2.333333334 = 6.388508355 x = 6.388508355 Simplifying x = 6.388508355Subproblem 2
x + -2.333333334 = -4.055175021 Simplifying x + -2.333333334 = -4.055175021 Reorder the terms: -2.333333334 + x = -4.055175021 Solving -2.333333334 + x = -4.055175021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.333333334' to each side of the equation. -2.333333334 + 2.333333334 + x = -4.055175021 + 2.333333334 Combine like terms: -2.333333334 + 2.333333334 = 0.000000000 0.000000000 + x = -4.055175021 + 2.333333334 x = -4.055175021 + 2.333333334 Combine like terms: -4.055175021 + 2.333333334 = -1.721841687 x = -1.721841687 Simplifying x = -1.721841687Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.388508355, -1.721841687}
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