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Simplifying -5x(x + 2) = -3(x + 1) + 7 Reorder the terms: -5x(2 + x) = -3(x + 1) + 7 (2 * -5x + x * -5x) = -3(x + 1) + 7 (-10x + -5x2) = -3(x + 1) + 7 Reorder the terms: -10x + -5x2 = -3(1 + x) + 7 -10x + -5x2 = (1 * -3 + x * -3) + 7 -10x + -5x2 = (-3 + -3x) + 7 Reorder the terms: -10x + -5x2 = -3 + 7 + -3x Combine like terms: -3 + 7 = 4 -10x + -5x2 = 4 + -3x Solving -10x + -5x2 = 4 + -3x Solving for variable 'x'. Reorder the terms: -4 + -10x + 3x + -5x2 = 4 + -3x + -4 + 3x Combine like terms: -10x + 3x = -7x -4 + -7x + -5x2 = 4 + -3x + -4 + 3x Reorder the terms: -4 + -7x + -5x2 = 4 + -4 + -3x + 3x Combine like terms: 4 + -4 = 0 -4 + -7x + -5x2 = 0 + -3x + 3x -4 + -7x + -5x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -4 + -7x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 7x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 7x + 5x2)' equal to zero and attempt to solve: Simplifying 4 + 7x + 5x2 = 0 Solving 4 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 1.4x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 1.4x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 1.4x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 1.4x + x2 = 0 + -0.8 1.4x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 1.4x + x2 = -0.8 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = -0.8 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -0.8 + 0.49 Combine like terms: -0.8 + 0.49 = -0.31 0.49 + 1.4x + x2 = -0.31 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = -0.31 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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