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Simplifying 5 + -2(3x2 + -2x) = x2 + 7 + -1x2 Reorder the terms: 5 + -2(-2x + 3x2) = x2 + 7 + -1x2 5 + (-2x * -2 + 3x2 * -2) = x2 + 7 + -1x2 5 + (4x + -6x2) = x2 + 7 + -1x2 Reorder the terms: 5 + 4x + -6x2 = 7 + x2 + -1x2 Combine like terms: x2 + -1x2 = 0 5 + 4x + -6x2 = 7 + 0 5 + 4x + -6x2 = 7 Solving 5 + 4x + -6x2 = 7 Solving for variable 'x'. Reorder the terms: 5 + -7 + 4x + -6x2 = 7 + -7 Combine like terms: 5 + -7 = -2 -2 + 4x + -6x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -2 + 4x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + 2x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + 2x + -3x2)' equal to zero and attempt to solve: Simplifying -1 + 2x + -3x2 = 0 Solving -1 + 2x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.3333333333 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -0.6666666667x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -0.6666666667x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -0.6666666667x + x2 = 0 + -0.3333333333 -0.6666666667x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -0.6666666667x + x2 = -0.3333333333 The x term is -0.6666666667x. Take half its coefficient (-0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. -0.6666666667x + 0.1111111112 + x2 = -0.3333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -0.3333333333 + 0.1111111112 Combine like terms: -0.3333333333 + 0.1111111112 = -0.2222222221 0.1111111112 + -0.6666666667x + x2 = -0.2222222221 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -0.2222222221 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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