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Simplifying x2 + -12x + -30 = 23 Reorder the terms: -30 + -12x + x2 = 23 Solving -30 + -12x + x2 = 23 Solving for variable 'x'. Reorder the terms: -30 + -23 + -12x + x2 = 23 + -23 Combine like terms: -30 + -23 = -53 -53 + -12x + x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -53 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + -12x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + -12x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + -12x + x2 = 0 + 53 -12x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 -12x + x2 = 53 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 = 53 + 36 Reorder the terms: 36 + -12x + x2 = 53 + 36 Combine like terms: 53 + 36 = 89 36 + -12x + x2 = 89 Factor a perfect square on the left side: (x + -6)(x + -6) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (x + -6) equal to 9.433981132 and -9.433981132.Subproblem 1
x + -6 = 9.433981132 Simplifying x + -6 = 9.433981132 Reorder the terms: -6 + x = 9.433981132 Solving -6 + x = 9.433981132 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 = 9.433981132 + 6 Combine like terms: -6 + 6 = 0 0 + x = 9.433981132 + 6 x = 9.433981132 + 6 Combine like terms: 9.433981132 + 6 = 15.433981132 x = 15.433981132 Simplifying x = 15.433981132Subproblem 2
x + -6 = -9.433981132 Simplifying x + -6 = -9.433981132 Reorder the terms: -6 + x = -9.433981132 Solving -6 + x = -9.433981132 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 = -9.433981132 + 6 Combine like terms: -6 + 6 = 0 0 + x = -9.433981132 + 6 x = -9.433981132 + 6 Combine like terms: -9.433981132 + 6 = -3.433981132 x = -3.433981132 Simplifying x = -3.433981132Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.433981132, -3.433981132}
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