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Simplifying -1[10x(3x + 3)] = -6 + -1[4(3x + -3) + -3x] Reorder the terms: -1[10x(3 + 3x)] = -6 + -1[4(3x + -3) + -3x] -1[(3 * 10x + 3x * 10x)] = -6 + -1[4(3x + -3) + -3x] -1[(30x + 30x2)] = -6 + -1[4(3x + -3) + -3x] [30x * -1 + 30x2 * -1] = -6 + -1[4(3x + -3) + -3x] [-30x + -30x2] = -6 + -1[4(3x + -3) + -3x] Reorder the terms: -30x + -30x2 = -6 + -1[4(-3 + 3x) + -3x] -30x + -30x2 = -6 + -1[(-3 * 4 + 3x * 4) + -3x] -30x + -30x2 = -6 + -1[(-12 + 12x) + -3x] Combine like terms: 12x + -3x = 9x -30x + -30x2 = -6 + -1[-12 + 9x] -30x + -30x2 = -6 + [-12 * -1 + 9x * -1] -30x + -30x2 = -6 + [12 + -9x] Combine like terms: -6 + 12 = 6 -30x + -30x2 = 6 + -9x Solving -30x + -30x2 = 6 + -9x Solving for variable 'x'. Reorder the terms: -6 + -30x + 9x + -30x2 = 6 + -9x + -6 + 9x Combine like terms: -30x + 9x = -21x -6 + -21x + -30x2 = 6 + -9x + -6 + 9x Reorder the terms: -6 + -21x + -30x2 = 6 + -6 + -9x + 9x Combine like terms: 6 + -6 = 0 -6 + -21x + -30x2 = 0 + -9x + 9x -6 + -21x + -30x2 = -9x + 9x Combine like terms: -9x + 9x = 0 -6 + -21x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(2 + 7x + 10x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(2 + 7x + 10x2)' equal to zero and attempt to solve: Simplifying 2 + 7x + 10x2 = 0 Solving 2 + 7x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.2 + 0.7x + x2 = 0.0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + 0.7x + -0.2 + x2 = 0.0 + -0.2 Reorder the terms: 0.2 + -0.2 + 0.7x + x2 = 0.0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + 0.7x + x2 = 0.0 + -0.2 0.7x + x2 = 0.0 + -0.2 Combine like terms: 0.0 + -0.2 = -0.2 0.7x + x2 = -0.2 The x term is 0.7x. Take half its coefficient (0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. 0.7x + 0.1225 + x2 = -0.2 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = -0.2 + 0.1225 Combine like terms: -0.2 + 0.1225 = -0.0775 0.1225 + 0.7x + x2 = -0.0775 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = -0.0775 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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