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Simplifying (3x2 + -2x + 15) + (3x2 + -2x + 8) = 7 Reorder the terms: (15 + -2x + 3x2) + (3x2 + -2x + 8) = 7 Remove parenthesis around (15 + -2x + 3x2) 15 + -2x + 3x2 + (3x2 + -2x + 8) = 7 Reorder the terms: 15 + -2x + 3x2 + (8 + -2x + 3x2) = 7 Remove parenthesis around (8 + -2x + 3x2) 15 + -2x + 3x2 + 8 + -2x + 3x2 = 7 Reorder the terms: 15 + 8 + -2x + -2x + 3x2 + 3x2 = 7 Combine like terms: 15 + 8 = 23 23 + -2x + -2x + 3x2 + 3x2 = 7 Combine like terms: -2x + -2x = -4x 23 + -4x + 3x2 + 3x2 = 7 Combine like terms: 3x2 + 3x2 = 6x2 23 + -4x + 6x2 = 7 Solving 23 + -4x + 6x2 = 7 Solving for variable 'x'. Reorder the terms: 23 + -7 + -4x + 6x2 = 7 + -7 Combine like terms: 23 + -7 = 16 16 + -4x + 6x2 = 7 + -7 Combine like terms: 7 + -7 = 0 16 + -4x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -2x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -2x + 3x2)' equal to zero and attempt to solve: Simplifying 8 + -2x + 3x2 = 0 Solving 8 + -2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + -0.6666666667x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -0.6666666667x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -0.6666666667x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -0.6666666667x + x2 = 0 + -2.666666667 -0.6666666667x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -0.6666666667x + x2 = -2.666666667 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 = -2.666666667 + 0.1111111112 Reorder the terms: 0.1111111112 + -0.6666666667x + x2 = -2.666666667 + 0.1111111112 Combine like terms: -2.666666667 + 0.1111111112 = -2.5555555558 0.1111111112 + -0.6666666667x + x2 = -2.5555555558 Factor a perfect square on the left side: (x + -0.3333333334)(x + -0.3333333334) = -2.5555555558 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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