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Simplifying 64x = 2(25x + 15x2 + 6) Reorder the terms: 64x = 2(6 + 25x + 15x2) 64x = (6 * 2 + 25x * 2 + 15x2 * 2) 64x = (12 + 50x + 30x2) Solving 64x = 12 + 50x + 30x2 Solving for variable 'x'. Reorder the terms: -12 + 64x + -50x + -30x2 = 12 + 50x + 30x2 + -12 + -50x + -30x2 Combine like terms: 64x + -50x = 14x -12 + 14x + -30x2 = 12 + 50x + 30x2 + -12 + -50x + -30x2 Reorder the terms: -12 + 14x + -30x2 = 12 + -12 + 50x + -50x + 30x2 + -30x2 Combine like terms: 12 + -12 = 0 -12 + 14x + -30x2 = 0 + 50x + -50x + 30x2 + -30x2 -12 + 14x + -30x2 = 50x + -50x + 30x2 + -30x2 Combine like terms: 50x + -50x = 0 -12 + 14x + -30x2 = 0 + 30x2 + -30x2 -12 + 14x + -30x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 -12 + 14x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 7x + -15x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 7x + -15x2)' equal to zero and attempt to solve: Simplifying -6 + 7x + -15x2 = 0 Solving -6 + 7x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. 0.4 + -0.4666666667x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -0.4666666667x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -0.4666666667x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -0.4666666667x + x2 = 0 + -0.4 -0.4666666667x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -0.4666666667x + x2 = -0.4 The x term is -0.4666666667x. Take half its coefficient (-0.2333333334). Square it (0.05444444448) and add it to both sides. Add '0.05444444448' to each side of the equation. -0.4666666667x + 0.05444444448 + x2 = -0.4 + 0.05444444448 Reorder the terms: 0.05444444448 + -0.4666666667x + x2 = -0.4 + 0.05444444448 Combine like terms: -0.4 + 0.05444444448 = -0.34555555552 0.05444444448 + -0.4666666667x + x2 = -0.34555555552 Factor a perfect square on the left side: (x + -0.2333333334)(x + -0.2333333334) = -0.34555555552 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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