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Simplifying (7x + -3)(3x + -7) = 90 Reorder the terms: (-3 + 7x)(3x + -7) = 90 Reorder the terms: (-3 + 7x)(-7 + 3x) = 90 Multiply (-3 + 7x) * (-7 + 3x) (-3(-7 + 3x) + 7x * (-7 + 3x)) = 90 ((-7 * -3 + 3x * -3) + 7x * (-7 + 3x)) = 90 ((21 + -9x) + 7x * (-7 + 3x)) = 90 (21 + -9x + (-7 * 7x + 3x * 7x)) = 90 (21 + -9x + (-49x + 21x2)) = 90 Combine like terms: -9x + -49x = -58x (21 + -58x + 21x2) = 90 Solving 21 + -58x + 21x2 = 90 Solving for variable 'x'. Reorder the terms: 21 + -90 + -58x + 21x2 = 90 + -90 Combine like terms: 21 + -90 = -69 -69 + -58x + 21x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -69 + -58x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -3.285714286 + -2.761904762x + x2 = 0 Move the constant term to the right: Add '3.285714286' to each side of the equation. -3.285714286 + -2.761904762x + 3.285714286 + x2 = 0 + 3.285714286 Reorder the terms: -3.285714286 + 3.285714286 + -2.761904762x + x2 = 0 + 3.285714286 Combine like terms: -3.285714286 + 3.285714286 = 0.000000000 0.000000000 + -2.761904762x + x2 = 0 + 3.285714286 -2.761904762x + x2 = 0 + 3.285714286 Combine like terms: 0 + 3.285714286 = 3.285714286 -2.761904762x + x2 = 3.285714286 The x term is -2.761904762x. Take half its coefficient (-1.380952381). Square it (1.907029479) and add it to both sides. Add '1.907029479' to each side of the equation. -2.761904762x + 1.907029479 + x2 = 3.285714286 + 1.907029479 Reorder the terms: 1.907029479 + -2.761904762x + x2 = 3.285714286 + 1.907029479 Combine like terms: 3.285714286 + 1.907029479 = 5.192743765 1.907029479 + -2.761904762x + x2 = 5.192743765 Factor a perfect square on the left side: (x + -1.380952381)(x + -1.380952381) = 5.192743765 Calculate the square root of the right side: 2.27875926 Break this problem into two subproblems by setting (x + -1.380952381) equal to 2.27875926 and -2.27875926.Subproblem 1
x + -1.380952381 = 2.27875926 Simplifying x + -1.380952381 = 2.27875926 Reorder the terms: -1.380952381 + x = 2.27875926 Solving -1.380952381 + x = 2.27875926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.380952381' to each side of the equation. -1.380952381 + 1.380952381 + x = 2.27875926 + 1.380952381 Combine like terms: -1.380952381 + 1.380952381 = 0.000000000 0.000000000 + x = 2.27875926 + 1.380952381 x = 2.27875926 + 1.380952381 Combine like terms: 2.27875926 + 1.380952381 = 3.659711641 x = 3.659711641 Simplifying x = 3.659711641Subproblem 2
x + -1.380952381 = -2.27875926 Simplifying x + -1.380952381 = -2.27875926 Reorder the terms: -1.380952381 + x = -2.27875926 Solving -1.380952381 + x = -2.27875926 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.380952381' to each side of the equation. -1.380952381 + 1.380952381 + x = -2.27875926 + 1.380952381 Combine like terms: -1.380952381 + 1.380952381 = 0.000000000 0.000000000 + x = -2.27875926 + 1.380952381 x = -2.27875926 + 1.380952381 Combine like terms: -2.27875926 + 1.380952381 = -0.897806879 x = -0.897806879 Simplifying x = -0.897806879Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.659711641, -0.897806879}
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