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Simplifying 8x + -1(22x + 7) = 5x(2x + -2) + 8 Reorder the terms: 8x + -1(7 + 22x) = 5x(2x + -2) + 8 8x + (7 * -1 + 22x * -1) = 5x(2x + -2) + 8 8x + (-7 + -22x) = 5x(2x + -2) + 8 Reorder the terms: -7 + 8x + -22x = 5x(2x + -2) + 8 Combine like terms: 8x + -22x = -14x -7 + -14x = 5x(2x + -2) + 8 Reorder the terms: -7 + -14x = 5x(-2 + 2x) + 8 -7 + -14x = (-2 * 5x + 2x * 5x) + 8 -7 + -14x = (-10x + 10x2) + 8 Reorder the terms: -7 + -14x = 8 + -10x + 10x2 Solving -7 + -14x = 8 + -10x + 10x2 Solving for variable 'x'. Reorder the terms: -7 + -8 + -14x + 10x + -10x2 = 8 + -10x + 10x2 + -8 + 10x + -10x2 Combine like terms: -7 + -8 = -15 -15 + -14x + 10x + -10x2 = 8 + -10x + 10x2 + -8 + 10x + -10x2 Combine like terms: -14x + 10x = -4x -15 + -4x + -10x2 = 8 + -10x + 10x2 + -8 + 10x + -10x2 Reorder the terms: -15 + -4x + -10x2 = 8 + -8 + -10x + 10x + 10x2 + -10x2 Combine like terms: 8 + -8 = 0 -15 + -4x + -10x2 = 0 + -10x + 10x + 10x2 + -10x2 -15 + -4x + -10x2 = -10x + 10x + 10x2 + -10x2 Combine like terms: -10x + 10x = 0 -15 + -4x + -10x2 = 0 + 10x2 + -10x2 -15 + -4x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 -15 + -4x + -10x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 4x + 10x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 4x + 10x2)' equal to zero and attempt to solve: Simplifying 15 + 4x + 10x2 = 0 Solving 15 + 4x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 1.5 + 0.4x + x2 = 0.0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 0.4x + -1.5 + x2 = 0.0 + -1.5 Reorder the terms: 1.5 + -1.5 + 0.4x + x2 = 0.0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 0.4x + x2 = 0.0 + -1.5 0.4x + x2 = 0.0 + -1.5 Combine like terms: 0.0 + -1.5 = -1.5 0.4x + x2 = -1.5 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = -1.5 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = -1.5 + 0.04 Combine like terms: -1.5 + 0.04 = -1.46 0.04 + 0.4x + x2 = -1.46 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = -1.46 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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