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Simplifying 12x + 10 = x2 Reorder the terms: 10 + 12x = x2 Solving 10 + 12x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 10 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -12x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -12x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -12x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -12x + x2 = 0 + 10 -12x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -12x + x2 = 10 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 = 10 + 36 Reorder the terms: 36 + -12x + x2 = 10 + 36 Combine like terms: 10 + 36 = 46 36 + -12x + x2 = 46 Factor a perfect square on the left side: (x + -6)(x + -6) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x + -6) equal to 6.782329983 and -6.782329983.Subproblem 1
x + -6 = 6.782329983 Simplifying x + -6 = 6.782329983 Reorder the terms: -6 + x = 6.782329983 Solving -6 + x = 6.782329983 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 = 6.782329983 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.782329983 + 6 x = 6.782329983 + 6 Combine like terms: 6.782329983 + 6 = 12.782329983 x = 12.782329983 Simplifying x = 12.782329983Subproblem 2
x + -6 = -6.782329983 Simplifying x + -6 = -6.782329983 Reorder the terms: -6 + x = -6.782329983 Solving -6 + x = -6.782329983 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 = -6.782329983 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.782329983 + 6 x = -6.782329983 + 6 Combine like terms: -6.782329983 + 6 = -0.782329983 x = -0.782329983 Simplifying x = -0.782329983Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.782329983, -0.782329983}
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