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Simplifying -2x(2x + 5) + -3 = -3(x + -1) Reorder the terms: -2x(5 + 2x) + -3 = -3(x + -1) (5 * -2x + 2x * -2x) + -3 = -3(x + -1) (-10x + -4x2) + -3 = -3(x + -1) Reorder the terms: -3 + -10x + -4x2 = -3(x + -1) Reorder the terms: -3 + -10x + -4x2 = -3(-1 + x) -3 + -10x + -4x2 = (-1 * -3 + x * -3) -3 + -10x + -4x2 = (3 + -3x) Solving -3 + -10x + -4x2 = 3 + -3x Solving for variable 'x'. Reorder the terms: -3 + -3 + -10x + 3x + -4x2 = 3 + -3x + -3 + 3x Combine like terms: -3 + -3 = -6 -6 + -10x + 3x + -4x2 = 3 + -3x + -3 + 3x Combine like terms: -10x + 3x = -7x -6 + -7x + -4x2 = 3 + -3x + -3 + 3x Reorder the terms: -6 + -7x + -4x2 = 3 + -3 + -3x + 3x Combine like terms: 3 + -3 = 0 -6 + -7x + -4x2 = 0 + -3x + 3x -6 + -7x + -4x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -6 + -7x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 7x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 7x + 4x2)' equal to zero and attempt to solve: Simplifying 6 + 7x + 4x2 = 0 Solving 6 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.5 + 1.75x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 1.75x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 1.75x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 1.75x + x2 = 0 + -1.5 1.75x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 1.75x + x2 = -1.5 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = -1.5 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = -1.5 + 0.765625 Combine like terms: -1.5 + 0.765625 = -0.734375 0.765625 + 1.75x + x2 = -0.734375 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = -0.734375 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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