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Simplifying 5(x + 5) + -5x(5 + -7x) = 0 Reorder the terms: 5(5 + x) + -5x(5 + -7x) = 0 (5 * 5 + x * 5) + -5x(5 + -7x) = 0 (25 + 5x) + -5x(5 + -7x) = 0 25 + 5x + (5 * -5x + -7x * -5x) = 0 25 + 5x + (-25x + 35x2) = 0 Combine like terms: 5x + -25x = -20x 25 + -20x + 35x2 = 0 Solving 25 + -20x + 35x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(5 + -4x + 7x2) = 0 Ignore the factor 5.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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