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Simplifying (12 + -1x) * 5x = 42 Reorder the terms for easier multiplication: 5x(12 + -1x) = 42 (12 * 5x + -1x * 5x) = 42 (60x + -5x2) = 42 Solving 60x + -5x2 = 42 Solving for variable 'x'. Reorder the terms: -42 + 60x + -5x2 = 42 + -42 Combine like terms: 42 + -42 = 0 -42 + 60x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 8.4 + -12x + x2 = 0 Move the constant term to the right: Add '-8.4' to each side of the equation. 8.4 + -12x + -8.4 + x2 = 0 + -8.4 Reorder the terms: 8.4 + -8.4 + -12x + x2 = 0 + -8.4 Combine like terms: 8.4 + -8.4 = 0.0 0.0 + -12x + x2 = 0 + -8.4 -12x + x2 = 0 + -8.4 Combine like terms: 0 + -8.4 = -8.4 -12x + x2 = -8.4 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -8.4 + 36 Reorder the terms: 36 + -12x + x2 = -8.4 + 36 Combine like terms: -8.4 + 36 = 27.6 36 + -12x + x2 = 27.6 Factor a perfect square on the left side: (x + -6)(x + -6) = 27.6 Calculate the square root of the right side: 5.253570215 Break this problem into two subproblems by setting (x + -6) equal to 5.253570215 and -5.253570215.Subproblem 1
x + -6 = 5.253570215 Simplifying x + -6 = 5.253570215 Reorder the terms: -6 + x = 5.253570215 Solving -6 + x = 5.253570215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.253570215 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.253570215 + 6 x = 5.253570215 + 6 Combine like terms: 5.253570215 + 6 = 11.253570215 x = 11.253570215 Simplifying x = 11.253570215Subproblem 2
x + -6 = -5.253570215 Simplifying x + -6 = -5.253570215 Reorder the terms: -6 + x = -5.253570215 Solving -6 + x = -5.253570215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.253570215 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.253570215 + 6 x = -5.253570215 + 6 Combine like terms: -5.253570215 + 6 = 0.746429785 x = 0.746429785 Simplifying x = 0.746429785Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.253570215, 0.746429785}
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