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Simplifying 6x + -7 = 5x(x + 3) Reorder the terms: -7 + 6x = 5x(x + 3) Reorder the terms: -7 + 6x = 5x(3 + x) -7 + 6x = (3 * 5x + x * 5x) -7 + 6x = (15x + 5x2) Solving -7 + 6x = 15x + 5x2 Solving for variable 'x'. Combine like terms: 6x + -15x = -9x -7 + -9x + -5x2 = 15x + 5x2 + -15x + -5x2 Reorder the terms: -7 + -9x + -5x2 = 15x + -15x + 5x2 + -5x2 Combine like terms: 15x + -15x = 0 -7 + -9x + -5x2 = 0 + 5x2 + -5x2 -7 + -9x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -7 + -9x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 9x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 9x + 5x2)' equal to zero and attempt to solve: Simplifying 7 + 9x + 5x2 = 0 Solving 7 + 9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + 1.8x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + 1.8x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + 1.8x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + 1.8x + x2 = 0 + -1.4 1.8x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 1.8x + x2 = -1.4 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = -1.4 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = -1.4 + 0.81 Combine like terms: -1.4 + 0.81 = -0.59 0.81 + 1.8x + x2 = -0.59 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = -0.59 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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