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Simplifying 7 + 5x(12 + x) = 112 7 + (12 * 5x + x * 5x) = 112 7 + (60x + 5x2) = 112 Solving 7 + 60x + 5x2 = 112 Solving for variable 'x'. Reorder the terms: 7 + -112 + 60x + 5x2 = 112 + -112 Combine like terms: 7 + -112 = -105 -105 + 60x + 5x2 = 112 + -112 Combine like terms: 112 + -112 = 0 -105 + 60x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-21 + 12x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-21 + 12x + x2)' equal to zero and attempt to solve: Simplifying -21 + 12x + x2 = 0 Solving -21 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + 12x + 21 + x2 = 0 + 21 Reorder the terms: -21 + 21 + 12x + x2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 12x + x2 = 0 + 21 12x + x2 = 0 + 21 Combine like terms: 0 + 21 = 21 12x + x2 = 21 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 = 21 + 36 Reorder the terms: 36 + 12x + x2 = 21 + 36 Combine like terms: 21 + 36 = 57 36 + 12x + x2 = 57 Factor a perfect square on the left side: (x + 6)(x + 6) = 57 Calculate the square root of the right side: 7.549834435 Break this problem into two subproblems by setting (x + 6) equal to 7.549834435 and -7.549834435.Subproblem 1
x + 6 = 7.549834435 Simplifying x + 6 = 7.549834435 Reorder the terms: 6 + x = 7.549834435 Solving 6 + x = 7.549834435 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 = 7.549834435 + -6 Combine like terms: 6 + -6 = 0 0 + x = 7.549834435 + -6 x = 7.549834435 + -6 Combine like terms: 7.549834435 + -6 = 1.549834435 x = 1.549834435 Simplifying x = 1.549834435Subproblem 2
x + 6 = -7.549834435 Simplifying x + 6 = -7.549834435 Reorder the terms: 6 + x = -7.549834435 Solving 6 + x = -7.549834435 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 = -7.549834435 + -6 Combine like terms: 6 + -6 = 0 0 + x = -7.549834435 + -6 x = -7.549834435 + -6 Combine like terms: -7.549834435 + -6 = -13.549834435 x = -13.549834435 Simplifying x = -13.549834435Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.549834435, -13.549834435}Solution
x = {1.549834435, -13.549834435}
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