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Simplifying (6x2 + 5) + -1(4x + -3) = 0 Reorder the terms: (5 + 6x2) + -1(4x + -3) = 0 Remove parenthesis around (5 + 6x2) 5 + 6x2 + -1(4x + -3) = 0 Reorder the terms: 5 + 6x2 + -1(-3 + 4x) = 0 5 + 6x2 + (-3 * -1 + 4x * -1) = 0 5 + 6x2 + (3 + -4x) = 0 Reorder the terms: 5 + 3 + -4x + 6x2 = 0 Combine like terms: 5 + 3 = 8 8 + -4x + 6x2 = 0 Solving 8 + -4x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -2x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + -2x + 3x2 = 0 Solving 4 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -0.6666666667x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -0.6666666667x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -0.6666666667x + x2 = 0 + -1.333333333 -0.6666666667x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -0.6666666667x + x2 = -1.333333333 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 = -1.333333333 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -1.333333333 + 0.1111111112 Combine like terms: -1.333333333 + 0.1111111112 = -1.2222222218 0.1111111112 + -0.6666666667x + x2 = -1.2222222218 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -1.2222222218 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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