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Simplifying 5x(4x + 8) = 4(6x + -10) Reorder the terms: 5x(8 + 4x) = 4(6x + -10) (8 * 5x + 4x * 5x) = 4(6x + -10) (40x + 20x2) = 4(6x + -10) Reorder the terms: 40x + 20x2 = 4(-10 + 6x) 40x + 20x2 = (-10 * 4 + 6x * 4) 40x + 20x2 = (-40 + 24x) Solving 40x + 20x2 = -40 + 24x Solving for variable 'x'. Reorder the terms: 40 + 40x + -24x + 20x2 = -40 + 24x + 40 + -24x Combine like terms: 40x + -24x = 16x 40 + 16x + 20x2 = -40 + 24x + 40 + -24x Reorder the terms: 40 + 16x + 20x2 = -40 + 40 + 24x + -24x Combine like terms: -40 + 40 = 0 40 + 16x + 20x2 = 0 + 24x + -24x 40 + 16x + 20x2 = 24x + -24x Combine like terms: 24x + -24x = 0 40 + 16x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(10 + 4x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(10 + 4x + 5x2)' equal to zero and attempt to solve: Simplifying 10 + 4x + 5x2 = 0 Solving 10 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + 0.8x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 0.8x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 0.8x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 0.8x + x2 = 0 + -2 0.8x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 0.8x + x2 = -2 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = -2 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = -2 + 0.16 Combine like terms: -2 + 0.16 = -1.84 0.16 + 0.8x + x2 = -1.84 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = -1.84 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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