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Simplifying 2x(5x + 3) + -1(8x + -2) = 0 Reorder the terms: 2x(3 + 5x) + -1(8x + -2) = 0 (3 * 2x + 5x * 2x) + -1(8x + -2) = 0 (6x + 10x2) + -1(8x + -2) = 0 Reorder the terms: 6x + 10x2 + -1(-2 + 8x) = 0 6x + 10x2 + (-2 * -1 + 8x * -1) = 0 6x + 10x2 + (2 + -8x) = 0 Reorder the terms: 2 + 6x + -8x + 10x2 = 0 Combine like terms: 6x + -8x = -2x 2 + -2x + 10x2 = 0 Solving 2 + -2x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -1x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -1x + 5x2)' equal to zero and attempt to solve: Simplifying 1 + -1x + 5x2 = 0 Solving 1 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -0.2x + x2 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -0.2x + -0.2 + x2 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -0.2x + x2 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -0.2x + x2 = 0 + -0.2 -0.2x + x2 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -0.2x + x2 = -0.2 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = -0.2 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = -0.2 + 0.01 Combine like terms: -0.2 + 0.01 = -0.19 0.01 + -0.2x + x2 = -0.19 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = -0.19 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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