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Simplifying 8x + -6x2 = 10 Solving 8x + -6x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 8x + -6x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 8x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 4x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 4x + -3x2)' equal to zero and attempt to solve: Simplifying -5 + 4x + -3x2 = 0 Solving -5 + 4x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 1.666666667 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -1.333333333x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -1.333333333x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + -1.666666667 -1.333333333x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -1.333333333x + x2 = -1.666666667 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = -1.666666667 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -1.666666667 + 0.4444444442 Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228 0.4444444442 + -1.333333333x + x2 = -1.2222222228 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = -1.2222222228 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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