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Simplifying 4x2 + -6x + -56 = 3x + -16 Reorder the terms: -56 + -6x + 4x2 = 3x + -16 Reorder the terms: -56 + -6x + 4x2 = -16 + 3x Solving -56 + -6x + 4x2 = -16 + 3x Solving for variable 'x'. Reorder the terms: -56 + 16 + -6x + -3x + 4x2 = -16 + 3x + 16 + -3x Combine like terms: -56 + 16 = -40 -40 + -6x + -3x + 4x2 = -16 + 3x + 16 + -3x Combine like terms: -6x + -3x = -9x -40 + -9x + 4x2 = -16 + 3x + 16 + -3x Reorder the terms: -40 + -9x + 4x2 = -16 + 16 + 3x + -3x Combine like terms: -16 + 16 = 0 -40 + -9x + 4x2 = 0 + 3x + -3x -40 + -9x + 4x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -40 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10 + -2.25x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -2.25x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -2.25x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -2.25x + x2 = 0 + 10 -2.25x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -2.25x + x2 = 10 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 10 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 10 + 1.265625 Combine like terms: 10 + 1.265625 = 11.265625 1.265625 + -2.25x + x2 = 11.265625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 11.265625 Calculate the square root of the right side: 3.356430396 Break this problem into two subproblems by setting (x + -1.125) equal to 3.356430396 and -3.356430396.Subproblem 1
x + -1.125 = 3.356430396 Simplifying x + -1.125 = 3.356430396 Reorder the terms: -1.125 + x = 3.356430396 Solving -1.125 + x = 3.356430396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 3.356430396 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 3.356430396 + 1.125 x = 3.356430396 + 1.125 Combine like terms: 3.356430396 + 1.125 = 4.481430396 x = 4.481430396 Simplifying x = 4.481430396Subproblem 2
x + -1.125 = -3.356430396 Simplifying x + -1.125 = -3.356430396 Reorder the terms: -1.125 + x = -3.356430396 Solving -1.125 + x = -3.356430396 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -3.356430396 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -3.356430396 + 1.125 x = -3.356430396 + 1.125 Combine like terms: -3.356430396 + 1.125 = -2.231430396 x = -2.231430396 Simplifying x = -2.231430396Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.481430396, -2.231430396}
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