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Simplifying 4x2 + 5(2) + (2x + -3)(8x) = 0 Multiply 5 * 2 4x2 + 10 + (2x + -3)(8x) = 0 Reorder the terms: 4x2 + 10 + (-3 + 2x)(8x) = 0 Remove parenthesis around (8x) 4x2 + 10 + (-3 + 2x) * 8x = 0 Reorder the terms for easier multiplication: 4x2 + 10 + 8x(-3 + 2x) = 0 4x2 + 10 + (-3 * 8x + 2x * 8x) = 0 4x2 + 10 + (-24x + 16x2) = 0 Reorder the terms: 10 + -24x + 4x2 + 16x2 = 0 Combine like terms: 4x2 + 16x2 = 20x2 10 + -24x + 20x2 = 0 Solving 10 + -24x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -12x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -12x + 10x2)' equal to zero and attempt to solve: Simplifying 5 + -12x + 10x2 = 0 Solving 5 + -12x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.5 + -1.2x + x2 = 0.0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.2x + -0.5 + x2 = 0.0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.2x + x2 = 0.0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.2x + x2 = 0.0 + -0.5 -1.2x + x2 = 0.0 + -0.5 Combine like terms: 0.0 + -0.5 = -0.5 -1.2x + x2 = -0.5 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = -0.5 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -0.5 + 0.36 Combine like terms: -0.5 + 0.36 = -0.14 0.36 + -1.2x + x2 = -0.14 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = -0.14 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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