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Simplifying (x + 12)(x + -30) + 26 = 0 Reorder the terms: (12 + x)(x + -30) + 26 = 0 Reorder the terms: (12 + x)(-30 + x) + 26 = 0 Multiply (12 + x) * (-30 + x) (12(-30 + x) + x(-30 + x)) + 26 = 0 ((-30 * 12 + x * 12) + x(-30 + x)) + 26 = 0 ((-360 + 12x) + x(-30 + x)) + 26 = 0 (-360 + 12x + (-30 * x + x * x)) + 26 = 0 (-360 + 12x + (-30x + x2)) + 26 = 0 Combine like terms: 12x + -30x = -18x (-360 + -18x + x2) + 26 = 0 Reorder the terms: -360 + 26 + -18x + x2 = 0 Combine like terms: -360 + 26 = -334 -334 + -18x + x2 = 0 Solving -334 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '334' to each side of the equation. -334 + -18x + 334 + x2 = 0 + 334 Reorder the terms: -334 + 334 + -18x + x2 = 0 + 334 Combine like terms: -334 + 334 = 0 0 + -18x + x2 = 0 + 334 -18x + x2 = 0 + 334 Combine like terms: 0 + 334 = 334 -18x + x2 = 334 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 334 + 81 Reorder the terms: 81 + -18x + x2 = 334 + 81 Combine like terms: 334 + 81 = 415 81 + -18x + x2 = 415 Factor a perfect square on the left side: (x + -9)(x + -9) = 415 Calculate the square root of the right side: 20.371548787 Break this problem into two subproblems by setting (x + -9) equal to 20.371548787 and -20.371548787.Subproblem 1
x + -9 = 20.371548787 Simplifying x + -9 = 20.371548787 Reorder the terms: -9 + x = 20.371548787 Solving -9 + x = 20.371548787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 20.371548787 + 9 Combine like terms: -9 + 9 = 0 0 + x = 20.371548787 + 9 x = 20.371548787 + 9 Combine like terms: 20.371548787 + 9 = 29.371548787 x = 29.371548787 Simplifying x = 29.371548787Subproblem 2
x + -9 = -20.371548787 Simplifying x + -9 = -20.371548787 Reorder the terms: -9 + x = -20.371548787 Solving -9 + x = -20.371548787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -20.371548787 + 9 Combine like terms: -9 + 9 = 0 0 + x = -20.371548787 + 9 x = -20.371548787 + 9 Combine like terms: -20.371548787 + 9 = -11.371548787 x = -11.371548787 Simplifying x = -11.371548787Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.371548787, -11.371548787}
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