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Simplifying 2x(5x + -15) = 10(x + -5) Reorder the terms: 2x(-15 + 5x) = 10(x + -5) (-15 * 2x + 5x * 2x) = 10(x + -5) (-30x + 10x2) = 10(x + -5) Reorder the terms: -30x + 10x2 = 10(-5 + x) -30x + 10x2 = (-5 * 10 + x * 10) -30x + 10x2 = (-50 + 10x) Solving -30x + 10x2 = -50 + 10x Solving for variable 'x'. Reorder the terms: 50 + -30x + -10x + 10x2 = -50 + 10x + 50 + -10x Combine like terms: -30x + -10x = -40x 50 + -40x + 10x2 = -50 + 10x + 50 + -10x Reorder the terms: 50 + -40x + 10x2 = -50 + 50 + 10x + -10x Combine like terms: -50 + 50 = 0 50 + -40x + 10x2 = 0 + 10x + -10x 50 + -40x + 10x2 = 10x + -10x Combine like terms: 10x + -10x = 0 50 + -40x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(5 + -4x + x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(5 + -4x + x2)' equal to zero and attempt to solve: Simplifying 5 + -4x + x2 = 0 Solving 5 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -4x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -4x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x + x2 = 0 + -5 -4x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4x + x2 = -5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -5 + 4 Reorder the terms: 4 + -4x + x2 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + -4x + x2 = -1 Factor a perfect square on the left side: (x + -2)(x + -2) = -1 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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