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Simplifying x(x + -4) + -14 = 130 + -2x Reorder the terms: x(-4 + x) + -14 = 130 + -2x (-4 * x + x * x) + -14 = 130 + -2x (-4x + x2) + -14 = 130 + -2x Reorder the terms: -14 + -4x + x2 = 130 + -2x Solving -14 + -4x + x2 = 130 + -2x Solving for variable 'x'. Reorder the terms: -14 + -130 + -4x + 2x + x2 = 130 + -2x + -130 + 2x Combine like terms: -14 + -130 = -144 -144 + -4x + 2x + x2 = 130 + -2x + -130 + 2x Combine like terms: -4x + 2x = -2x -144 + -2x + x2 = 130 + -2x + -130 + 2x Reorder the terms: -144 + -2x + x2 = 130 + -130 + -2x + 2x Combine like terms: 130 + -130 = 0 -144 + -2x + x2 = 0 + -2x + 2x -144 + -2x + x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -144 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -2x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -2x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -2x + x2 = 0 + 144 -2x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -2x + x2 = 144 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 144 + 1 Reorder the terms: 1 + -2x + x2 = 144 + 1 Combine like terms: 144 + 1 = 145 1 + -2x + x2 = 145 Factor a perfect square on the left side: (x + -1)(x + -1) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + -1) equal to 12.041594579 and -12.041594579.Subproblem 1
x + -1 = 12.041594579 Simplifying x + -1 = 12.041594579 Reorder the terms: -1 + x = 12.041594579 Solving -1 + x = 12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 12.041594579 + 1 Combine like terms: -1 + 1 = 0 0 + x = 12.041594579 + 1 x = 12.041594579 + 1 Combine like terms: 12.041594579 + 1 = 13.041594579 x = 13.041594579 Simplifying x = 13.041594579Subproblem 2
x + -1 = -12.041594579 Simplifying x + -1 = -12.041594579 Reorder the terms: -1 + x = -12.041594579 Solving -1 + x = -12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -12.041594579 + 1 Combine like terms: -1 + 1 = 0 0 + x = -12.041594579 + 1 x = -12.041594579 + 1 Combine like terms: -12.041594579 + 1 = -11.041594579 x = -11.041594579 Simplifying x = -11.041594579Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.041594579, -11.041594579}
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