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Simplifying 15x(-7x + 6) = 11 + -1(x + -10) Reorder the terms: 15x(6 + -7x) = 11 + -1(x + -10) (6 * 15x + -7x * 15x) = 11 + -1(x + -10) (90x + -105x2) = 11 + -1(x + -10) Reorder the terms: 90x + -105x2 = 11 + -1(-10 + x) 90x + -105x2 = 11 + (-10 * -1 + x * -1) 90x + -105x2 = 11 + (10 + -1x) Combine like terms: 11 + 10 = 21 90x + -105x2 = 21 + -1x Solving 90x + -105x2 = 21 + -1x Solving for variable 'x'. Reorder the terms: -21 + 90x + x + -105x2 = 21 + -1x + -21 + x Combine like terms: 90x + x = 91x -21 + 91x + -105x2 = 21 + -1x + -21 + x Reorder the terms: -21 + 91x + -105x2 = 21 + -21 + -1x + x Combine like terms: 21 + -21 = 0 -21 + 91x + -105x2 = 0 + -1x + x -21 + 91x + -105x2 = -1x + x Combine like terms: -1x + x = 0 -21 + 91x + -105x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-3 + 13x + -15x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-3 + 13x + -15x2)' equal to zero and attempt to solve: Simplifying -3 + 13x + -15x2 = 0 Solving -3 + 13x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. 0.2 + -0.8666666667x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -0.8666666667x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -0.8666666667x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -0.8666666667x + x2 = 0 + -0.2 -0.8666666667x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -0.8666666667x + x2 = -0.2 The x term is -0.8666666667x. Take half its coefficient (-0.4333333334). Square it (0.1877777778) and add it to both sides. Add '0.1877777778' to each side of the equation. -0.8666666667x + 0.1877777778 + x2 = -0.2 + 0.1877777778 Reorder the terms: 0.1877777778 + -0.8666666667x + x2 = -0.2 + 0.1877777778 Combine like terms: -0.2 + 0.1877777778 = -0.0122222222 0.1877777778 + -0.8666666667x + x2 = -0.0122222222 Factor a perfect square on the left side: (x + -0.4333333334)(x + -0.4333333334) = -0.0122222222 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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