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Simplifying -10x2 = 11 + 7x Solving -10x2 = 11 + 7x Solving for variable 'x'. Reorder the terms: -11 + -7x + -10x2 = 11 + 7x + -11 + -7x Reorder the terms: -11 + -7x + -10x2 = 11 + -11 + 7x + -7x Combine like terms: 11 + -11 = 0 -11 + -7x + -10x2 = 0 + 7x + -7x -11 + -7x + -10x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -11 + -7x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 7x + 10x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 7x + 10x2)' equal to zero and attempt to solve: Simplifying 11 + 7x + 10x2 = 0 Solving 11 + 7x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.1 + 0.7x + x2 = 0.0 Move the constant term to the right: Add '-1.1' to each side of the equation. 1.1 + 0.7x + -1.1 + x2 = 0.0 + -1.1 Reorder the terms: 1.1 + -1.1 + 0.7x + x2 = 0.0 + -1.1 Combine like terms: 1.1 + -1.1 = 0.0 0.0 + 0.7x + x2 = 0.0 + -1.1 0.7x + x2 = 0.0 + -1.1 Combine like terms: 0.0 + -1.1 = -1.1 0.7x + x2 = -1.1 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 = -1.1 + 0.1225 Reorder the terms: 0.1225 + 0.7x + x2 = -1.1 + 0.1225 Combine like terms: -1.1 + 0.1225 = -0.9775 0.1225 + 0.7x + x2 = -0.9775 Factor a perfect square on the left side: (x + 0.35)(x + 0.35) = -0.9775 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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