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Simplifying -7x(2x + 1) + 3(5x + -4) = 0 Reorder the terms: -7x(1 + 2x) + 3(5x + -4) = 0 (1 * -7x + 2x * -7x) + 3(5x + -4) = 0 (-7x + -14x2) + 3(5x + -4) = 0 Reorder the terms: -7x + -14x2 + 3(-4 + 5x) = 0 -7x + -14x2 + (-4 * 3 + 5x * 3) = 0 -7x + -14x2 + (-12 + 15x) = 0 Reorder the terms: -12 + -7x + 15x + -14x2 = 0 Combine like terms: -7x + 15x = 8x -12 + 8x + -14x2 = 0 Solving -12 + 8x + -14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 4x + -7x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 4x + -7x2)' equal to zero and attempt to solve: Simplifying -6 + 4x + -7x2 = 0 Solving -6 + 4x + -7x2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. 0.8571428571 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '-0.8571428571' to each side of the equation. 0.8571428571 + -0.5714285714x + -0.8571428571 + x2 = 0 + -0.8571428571 Reorder the terms: 0.8571428571 + -0.8571428571 + -0.5714285714x + x2 = 0 + -0.8571428571 Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000 0.0000000000 + -0.5714285714x + x2 = 0 + -0.8571428571 -0.5714285714x + x2 = 0 + -0.8571428571 Combine like terms: 0 + -0.8571428571 = -0.8571428571 -0.5714285714x + x2 = -0.8571428571 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 = -0.8571428571 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = -0.8571428571 + 0.08163265305 Combine like terms: -0.8571428571 + 0.08163265305 = -0.77551020405 0.08163265305 + -0.5714285714x + x2 = -0.77551020405 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = -0.77551020405 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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