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Simplifying (2x + -7)(7x + 2) = 49 + 7x Reorder the terms: (-7 + 2x)(7x + 2) = 49 + 7x Reorder the terms: (-7 + 2x)(2 + 7x) = 49 + 7x Multiply (-7 + 2x) * (2 + 7x) (-7(2 + 7x) + 2x * (2 + 7x)) = 49 + 7x ((2 * -7 + 7x * -7) + 2x * (2 + 7x)) = 49 + 7x ((-14 + -49x) + 2x * (2 + 7x)) = 49 + 7x (-14 + -49x + (2 * 2x + 7x * 2x)) = 49 + 7x (-14 + -49x + (4x + 14x2)) = 49 + 7x Combine like terms: -49x + 4x = -45x (-14 + -45x + 14x2) = 49 + 7x Solving -14 + -45x + 14x2 = 49 + 7x Solving for variable 'x'. Reorder the terms: -14 + -49 + -45x + -7x + 14x2 = 49 + 7x + -49 + -7x Combine like terms: -14 + -49 = -63 -63 + -45x + -7x + 14x2 = 49 + 7x + -49 + -7x Combine like terms: -45x + -7x = -52x -63 + -52x + 14x2 = 49 + 7x + -49 + -7x Reorder the terms: -63 + -52x + 14x2 = 49 + -49 + 7x + -7x Combine like terms: 49 + -49 = 0 -63 + -52x + 14x2 = 0 + 7x + -7x -63 + -52x + 14x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -63 + -52x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -4.5 + -3.714285714x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -3.714285714x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -3.714285714x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -3.714285714x + x2 = 0 + 4.5 -3.714285714x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -3.714285714x + x2 = 4.5 The x term is -3.714285714x. Take half its coefficient (-1.857142857). Square it (3.448979591) and add it to both sides. Add '3.448979591' to each side of the equation. -3.714285714x + 3.448979591 + x2 = 4.5 + 3.448979591 Reorder the terms: 3.448979591 + -3.714285714x + x2 = 4.5 + 3.448979591 Combine like terms: 4.5 + 3.448979591 = 7.948979591 3.448979591 + -3.714285714x + x2 = 7.948979591 Factor a perfect square on the left side: (x + -1.857142857)(x + -1.857142857) = 7.948979591 Calculate the square root of the right side: 2.819393479 Break this problem into two subproblems by setting (x + -1.857142857) equal to 2.819393479 and -2.819393479.Subproblem 1
x + -1.857142857 = 2.819393479 Simplifying x + -1.857142857 = 2.819393479 Reorder the terms: -1.857142857 + x = 2.819393479 Solving -1.857142857 + x = 2.819393479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.857142857' to each side of the equation. -1.857142857 + 1.857142857 + x = 2.819393479 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + x = 2.819393479 + 1.857142857 x = 2.819393479 + 1.857142857 Combine like terms: 2.819393479 + 1.857142857 = 4.676536336 x = 4.676536336 Simplifying x = 4.676536336Subproblem 2
x + -1.857142857 = -2.819393479 Simplifying x + -1.857142857 = -2.819393479 Reorder the terms: -1.857142857 + x = -2.819393479 Solving -1.857142857 + x = -2.819393479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.857142857' to each side of the equation. -1.857142857 + 1.857142857 + x = -2.819393479 + 1.857142857 Combine like terms: -1.857142857 + 1.857142857 = 0.000000000 0.000000000 + x = -2.819393479 + 1.857142857 x = -2.819393479 + 1.857142857 Combine like terms: -2.819393479 + 1.857142857 = -0.962250622 x = -0.962250622 Simplifying x = -0.962250622Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.676536336, -0.962250622}
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