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Simplifying 2x + -3(2x + 5) + -1x(2 + 7x) = 9 Reorder the terms: 2x + -3(5 + 2x) + -1x(2 + 7x) = 9 2x + (5 * -3 + 2x * -3) + -1x(2 + 7x) = 9 2x + (-15 + -6x) + -1x(2 + 7x) = 9 2x + -15 + -6x + (2 * -1x + 7x * -1x) = 9 2x + -15 + -6x + (-2x + -7x2) = 9 Reorder the terms: -15 + 2x + -6x + -2x + -7x2 = 9 Combine like terms: 2x + -6x = -4x -15 + -4x + -2x + -7x2 = 9 Combine like terms: -4x + -2x = -6x -15 + -6x + -7x2 = 9 Solving -15 + -6x + -7x2 = 9 Solving for variable 'x'. Reorder the terms: -15 + -9 + -6x + -7x2 = 9 + -9 Combine like terms: -15 + -9 = -24 -24 + -6x + -7x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -24 + -6x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + 6x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(24 + 6x + 7x2)' equal to zero and attempt to solve: Simplifying 24 + 6x + 7x2 = 0 Solving 24 + 6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 3.428571429 + 0.8571428571x + x2 = 0 Move the constant term to the right: Add '-3.428571429' to each side of the equation. 3.428571429 + 0.8571428571x + -3.428571429 + x2 = 0 + -3.428571429 Reorder the terms: 3.428571429 + -3.428571429 + 0.8571428571x + x2 = 0 + -3.428571429 Combine like terms: 3.428571429 + -3.428571429 = 0.000000000 0.000000000 + 0.8571428571x + x2 = 0 + -3.428571429 0.8571428571x + x2 = 0 + -3.428571429 Combine like terms: 0 + -3.428571429 = -3.428571429 0.8571428571x + x2 = -3.428571429 The x term is 0.8571428571x. Take half its coefficient (0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. 0.8571428571x + 0.1836734694 + x2 = -3.428571429 + 0.1836734694 Reorder the terms: 0.1836734694 + 0.8571428571x + x2 = -3.428571429 + 0.1836734694 Combine like terms: -3.428571429 + 0.1836734694 = -3.2448979596 0.1836734694 + 0.8571428571x + x2 = -3.2448979596 Factor a perfect square on the left side: (x + 0.4285714286)(x + 0.4285714286) = -3.2448979596 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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