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Simplifying 13x(5x + -2x) = 5(3x + -1) Combine like terms: 5x + -2x = 3x 13x(3x) = 5(3x + -1) Remove parenthesis around (3x) 13x * 3x = 5(3x + -1) Reorder the terms for easier multiplication: 13 * 3x * x = 5(3x + -1) Multiply 13 * 3 39x * x = 5(3x + -1) Multiply x * x 39x2 = 5(3x + -1) Reorder the terms: 39x2 = 5(-1 + 3x) 39x2 = (-1 * 5 + 3x * 5) 39x2 = (-5 + 15x) Solving 39x2 = -5 + 15x Solving for variable 'x'. Reorder the terms: 5 + -15x + 39x2 = -5 + 15x + 5 + -15x Reorder the terms: 5 + -15x + 39x2 = -5 + 5 + 15x + -15x Combine like terms: -5 + 5 = 0 5 + -15x + 39x2 = 0 + 15x + -15x 5 + -15x + 39x2 = 15x + -15x Combine like terms: 15x + -15x = 0 5 + -15x + 39x2 = 0 Begin completing the square. Divide all terms by 39 the coefficient of the squared term: Divide each side by '39'. 0.1282051282 + -0.3846153846x + x2 = 0 Move the constant term to the right: Add '-0.1282051282' to each side of the equation. 0.1282051282 + -0.3846153846x + -0.1282051282 + x2 = 0 + -0.1282051282 Reorder the terms: 0.1282051282 + -0.1282051282 + -0.3846153846x + x2 = 0 + -0.1282051282 Combine like terms: 0.1282051282 + -0.1282051282 = 0.0000000000 0.0000000000 + -0.3846153846x + x2 = 0 + -0.1282051282 -0.3846153846x + x2 = 0 + -0.1282051282 Combine like terms: 0 + -0.1282051282 = -0.1282051282 -0.3846153846x + x2 = -0.1282051282 The x term is -0.3846153846x. Take half its coefficient (-0.1923076923). Square it (0.03698224852) and add it to both sides. Add '0.03698224852' to each side of the equation. -0.3846153846x + 0.03698224852 + x2 = -0.1282051282 + 0.03698224852 Reorder the terms: 0.03698224852 + -0.3846153846x + x2 = -0.1282051282 + 0.03698224852 Combine like terms: -0.1282051282 + 0.03698224852 = -0.09122287968 0.03698224852 + -0.3846153846x + x2 = -0.09122287968 Factor a perfect square on the left side: (x + -0.1923076923)(x + -0.1923076923) = -0.09122287968 Can't calculate square root of the right side. The solution to this equation could not be determined.
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