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Simplifying (x + -7)(x + 9) + (-8x + -9)(x + 5) = 0 Reorder the terms: (-7 + x)(x + 9) + (-8x + -9)(x + 5) = 0 Reorder the terms: (-7 + x)(9 + x) + (-8x + -9)(x + 5) = 0 Multiply (-7 + x) * (9 + x) (-7(9 + x) + x(9 + x)) + (-8x + -9)(x + 5) = 0 ((9 * -7 + x * -7) + x(9 + x)) + (-8x + -9)(x + 5) = 0 ((-63 + -7x) + x(9 + x)) + (-8x + -9)(x + 5) = 0 (-63 + -7x + (9 * x + x * x)) + (-8x + -9)(x + 5) = 0 (-63 + -7x + (9x + x2)) + (-8x + -9)(x + 5) = 0 Combine like terms: -7x + 9x = 2x (-63 + 2x + x2) + (-8x + -9)(x + 5) = 0 Reorder the terms: -63 + 2x + x2 + (-9 + -8x)(x + 5) = 0 Reorder the terms: -63 + 2x + x2 + (-9 + -8x)(5 + x) = 0 Multiply (-9 + -8x) * (5 + x) -63 + 2x + x2 + (-9(5 + x) + -8x * (5 + x)) = 0 -63 + 2x + x2 + ((5 * -9 + x * -9) + -8x * (5 + x)) = 0 -63 + 2x + x2 + ((-45 + -9x) + -8x * (5 + x)) = 0 -63 + 2x + x2 + (-45 + -9x + (5 * -8x + x * -8x)) = 0 -63 + 2x + x2 + (-45 + -9x + (-40x + -8x2)) = 0 Combine like terms: -9x + -40x = -49x -63 + 2x + x2 + (-45 + -49x + -8x2) = 0 Reorder the terms: -63 + -45 + 2x + -49x + x2 + -8x2 = 0 Combine like terms: -63 + -45 = -108 -108 + 2x + -49x + x2 + -8x2 = 0 Combine like terms: 2x + -49x = -47x -108 + -47x + x2 + -8x2 = 0 Combine like terms: x2 + -8x2 = -7x2 -108 + -47x + -7x2 = 0 Solving -108 + -47x + -7x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(108 + 47x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(108 + 47x + 7x2)' equal to zero and attempt to solve: Simplifying 108 + 47x + 7x2 = 0 Solving 108 + 47x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 15.42857143 + 6.714285714x + x2 = 0 Move the constant term to the right: Add '-15.42857143' to each side of the equation. 15.42857143 + 6.714285714x + -15.42857143 + x2 = 0 + -15.42857143 Reorder the terms: 15.42857143 + -15.42857143 + 6.714285714x + x2 = 0 + -15.42857143 Combine like terms: 15.42857143 + -15.42857143 = 0.00000000 0.00000000 + 6.714285714x + x2 = 0 + -15.42857143 6.714285714x + x2 = 0 + -15.42857143 Combine like terms: 0 + -15.42857143 = -15.42857143 6.714285714x + x2 = -15.42857143 The x term is 6.714285714x. Take half its coefficient (3.357142857). Square it (11.27040816) and add it to both sides. Add '11.27040816' to each side of the equation. 6.714285714x + 11.27040816 + x2 = -15.42857143 + 11.27040816 Reorder the terms: 11.27040816 + 6.714285714x + x2 = -15.42857143 + 11.27040816 Combine like terms: -15.42857143 + 11.27040816 = -4.15816327 11.27040816 + 6.714285714x + x2 = -4.15816327 Factor a perfect square on the left side: (x + 3.357142857)(x + 3.357142857) = -4.15816327 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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