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Simplifying 0 = 14x2 + 38x + 186 Reorder the terms: 0 = 186 + 38x + 14x2 Solving 0 = 186 + 38x + 14x2 Solving for variable 'x'. Combine like terms: 0 + -186 = -186 -186 + -38x + -14x2 = 186 + 38x + 14x2 + -186 + -38x + -14x2 Reorder the terms: -186 + -38x + -14x2 = 186 + -186 + 38x + -38x + 14x2 + -14x2 Combine like terms: 186 + -186 = 0 -186 + -38x + -14x2 = 0 + 38x + -38x + 14x2 + -14x2 -186 + -38x + -14x2 = 38x + -38x + 14x2 + -14x2 Combine like terms: 38x + -38x = 0 -186 + -38x + -14x2 = 0 + 14x2 + -14x2 -186 + -38x + -14x2 = 14x2 + -14x2 Combine like terms: 14x2 + -14x2 = 0 -186 + -38x + -14x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(93 + 19x + 7x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(93 + 19x + 7x2)' equal to zero and attempt to solve: Simplifying 93 + 19x + 7x2 = 0 Solving 93 + 19x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 13.28571429 + 2.714285714x + x2 = 0 Move the constant term to the right: Add '-13.28571429' to each side of the equation. 13.28571429 + 2.714285714x + -13.28571429 + x2 = 0 + -13.28571429 Reorder the terms: 13.28571429 + -13.28571429 + 2.714285714x + x2 = 0 + -13.28571429 Combine like terms: 13.28571429 + -13.28571429 = 0.00000000 0.00000000 + 2.714285714x + x2 = 0 + -13.28571429 2.714285714x + x2 = 0 + -13.28571429 Combine like terms: 0 + -13.28571429 = -13.28571429 2.714285714x + x2 = -13.28571429 The x term is 2.714285714x. Take half its coefficient (1.357142857). Square it (1.841836734) and add it to both sides. Add '1.841836734' to each side of the equation. 2.714285714x + 1.841836734 + x2 = -13.28571429 + 1.841836734 Reorder the terms: 1.841836734 + 2.714285714x + x2 = -13.28571429 + 1.841836734 Combine like terms: -13.28571429 + 1.841836734 = -11.443877556 1.841836734 + 2.714285714x + x2 = -11.443877556 Factor a perfect square on the left side: (x + 1.357142857)(x + 1.357142857) = -11.443877556 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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