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Simplifying -3x(5 + 7x) = 4x + 6 (5 * -3x + 7x * -3x) = 4x + 6 (-15x + -21x2) = 4x + 6 Reorder the terms: -15x + -21x2 = 6 + 4x Solving -15x + -21x2 = 6 + 4x Solving for variable 'x'. Reorder the terms: -6 + -15x + -4x + -21x2 = 6 + 4x + -6 + -4x Combine like terms: -15x + -4x = -19x -6 + -19x + -21x2 = 6 + 4x + -6 + -4x Reorder the terms: -6 + -19x + -21x2 = 6 + -6 + 4x + -4x Combine like terms: 6 + -6 = 0 -6 + -19x + -21x2 = 0 + 4x + -4x -6 + -19x + -21x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -6 + -19x + -21x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 19x + 21x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 19x + 21x2)' equal to zero and attempt to solve: Simplifying 6 + 19x + 21x2 = 0 Solving 6 + 19x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.2857142857 + 0.9047619048x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 0.9047619048x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 0.9047619048x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 0.9047619048x + x2 = 0 + -0.2857142857 0.9047619048x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 0.9047619048x + x2 = -0.2857142857 The x term is 0.9047619048x. Take half its coefficient (0.4523809524). Square it (0.2046485261) and add it to both sides. Add '0.2046485261' to each side of the equation. 0.9047619048x + 0.2046485261 + x2 = -0.2857142857 + 0.2046485261 Reorder the terms: 0.2046485261 + 0.9047619048x + x2 = -0.2857142857 + 0.2046485261 Combine like terms: -0.2857142857 + 0.2046485261 = -0.0810657596 0.2046485261 + 0.9047619048x + x2 = -0.0810657596 Factor a perfect square on the left side: (x + 0.4523809524)(x + 0.4523809524) = -0.0810657596 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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