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Simplifying 9x2 + -42x + 49 = -20 Reorder the terms: 49 + -42x + 9x2 = -20 Solving 49 + -42x + 9x2 = -20 Solving for variable 'x'. Reorder the terms: 49 + 20 + -42x + 9x2 = -20 + 20 Combine like terms: 49 + 20 = 69 69 + -42x + 9x2 = -20 + 20 Combine like terms: -20 + 20 = 0 69 + -42x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(23 + -14x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(23 + -14x + 3x2)' equal to zero and attempt to solve: Simplifying 23 + -14x + 3x2 = 0 Solving 23 + -14x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7.666666667 + -4.666666667x + x2 = 0 Move the constant term to the right: Add '-7.666666667' to each side of the equation. 7.666666667 + -4.666666667x + -7.666666667 + x2 = 0 + -7.666666667 Reorder the terms: 7.666666667 + -7.666666667 + -4.666666667x + x2 = 0 + -7.666666667 Combine like terms: 7.666666667 + -7.666666667 = 0.000000000 0.000000000 + -4.666666667x + x2 = 0 + -7.666666667 -4.666666667x + x2 = 0 + -7.666666667 Combine like terms: 0 + -7.666666667 = -7.666666667 -4.666666667x + x2 = -7.666666667 The x term is -4.666666667x. Take half its coefficient (-2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. -4.666666667x + 5.444444448 + x2 = -7.666666667 + 5.444444448 Reorder the terms: 5.444444448 + -4.666666667x + x2 = -7.666666667 + 5.444444448 Combine like terms: -7.666666667 + 5.444444448 = -2.222222219 5.444444448 + -4.666666667x + x2 = -2.222222219 Factor a perfect square on the left side: (x + -2.333333334)(x + -2.333333334) = -2.222222219 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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