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Simplifying -14x2 + -17x + -23 = 0 Reorder the terms: -23 + -17x + -14x2 = 0 Solving -23 + -17x + -14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(23 + 17x + 14x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(23 + 17x + 14x2)' equal to zero and attempt to solve: Simplifying 23 + 17x + 14x2 = 0 Solving 23 + 17x + 14x2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 1.642857143 + 1.214285714x + x2 = 0 Move the constant term to the right: Add '-1.642857143' to each side of the equation. 1.642857143 + 1.214285714x + -1.642857143 + x2 = 0 + -1.642857143 Reorder the terms: 1.642857143 + -1.642857143 + 1.214285714x + x2 = 0 + -1.642857143 Combine like terms: 1.642857143 + -1.642857143 = 0.000000000 0.000000000 + 1.214285714x + x2 = 0 + -1.642857143 1.214285714x + x2 = 0 + -1.642857143 Combine like terms: 0 + -1.642857143 = -1.642857143 1.214285714x + x2 = -1.642857143 The x term is 1.214285714x. Take half its coefficient (0.607142857). Square it (0.3686224488) and add it to both sides. Add '0.3686224488' to each side of the equation. 1.214285714x + 0.3686224488 + x2 = -1.642857143 + 0.3686224488 Reorder the terms: 0.3686224488 + 1.214285714x + x2 = -1.642857143 + 0.3686224488 Combine like terms: -1.642857143 + 0.3686224488 = -1.2742346942 0.3686224488 + 1.214285714x + x2 = -1.2742346942 Factor a perfect square on the left side: (x + 0.607142857)(x + 0.607142857) = -1.2742346942 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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