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Simplifying 0 = 7x2 + 4x + 5 Reorder the terms: 0 = 5 + 4x + 7x2 Solving 0 = 5 + 4x + 7x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -4x + -7x2 = 5 + 4x + 7x2 + -5 + -4x + -7x2 Reorder the terms: -5 + -4x + -7x2 = 5 + -5 + 4x + -4x + 7x2 + -7x2 Combine like terms: 5 + -5 = 0 -5 + -4x + -7x2 = 0 + 4x + -4x + 7x2 + -7x2 -5 + -4x + -7x2 = 4x + -4x + 7x2 + -7x2 Combine like terms: 4x + -4x = 0 -5 + -4x + -7x2 = 0 + 7x2 + -7x2 -5 + -4x + -7x2 = 7x2 + -7x2 Combine like terms: 7x2 + -7x2 = 0 -5 + -4x + -7x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 4x + 7x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 4x + 7x2)' equal to zero and attempt to solve: Simplifying 5 + 4x + 7x2 = 0 Solving 5 + 4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.7142857143 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + 0.5714285714x + -0.7142857143 + x2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + 0.5714285714x + x2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + 0.5714285714x + x2 = 0 + -0.7142857143 0.5714285714x + x2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 0.5714285714x + x2 = -0.7142857143 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = -0.7142857143 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = -0.7142857143 + 0.08163265305 Combine like terms: -0.7142857143 + 0.08163265305 = -0.63265306125 0.08163265305 + 0.5714285714x + x2 = -0.63265306125 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = -0.63265306125 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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