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Simplifying 3x * 2 = 2x * 2x + 10 Reorder the terms for easier multiplication: 3 * 2x = 2x * 2x + 10 Multiply 3 * 2 6x = 2x * 2x + 10 Reorder the terms for easier multiplication: 6x = 2 * 2x * x + 10 Multiply 2 * 2 6x = 4x * x + 10 Multiply x * x 6x = 4x2 + 10 Reorder the terms: 6x = 10 + 4x2 Solving 6x = 10 + 4x2 Solving for variable 'x'. Reorder the terms: -10 + 6x + -4x2 = 10 + 4x2 + -10 + -4x2 Reorder the terms: -10 + 6x + -4x2 = 10 + -10 + 4x2 + -4x2 Combine like terms: 10 + -10 = 0 -10 + 6x + -4x2 = 0 + 4x2 + -4x2 -10 + 6x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -10 + 6x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + 3x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + 3x + -2x2)' equal to zero and attempt to solve: Simplifying -5 + 3x + -2x2 = 0 Solving -5 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -1.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -1.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -1.5x + x2 = 0 + -2.5 -1.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -1.5x + x2 = -2.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -2.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -2.5 + 0.5625 Combine like terms: -2.5 + 0.5625 = -1.9375 0.5625 + -1.5x + x2 = -1.9375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -1.9375 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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