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Simplifying x2 + -4x + -56 = 3 Reorder the terms: -56 + -4x + x2 = 3 Solving -56 + -4x + x2 = 3 Solving for variable 'x'. Reorder the terms: -56 + -3 + -4x + x2 = 3 + -3 Combine like terms: -56 + -3 = -59 -59 + -4x + x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -59 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '59' to each side of the equation. -59 + -4x + 59 + x2 = 0 + 59 Reorder the terms: -59 + 59 + -4x + x2 = 0 + 59 Combine like terms: -59 + 59 = 0 0 + -4x + x2 = 0 + 59 -4x + x2 = 0 + 59 Combine like terms: 0 + 59 = 59 -4x + x2 = 59 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 59 + 4 Reorder the terms: 4 + -4x + x2 = 59 + 4 Combine like terms: 59 + 4 = 63 4 + -4x + x2 = 63 Factor a perfect square on the left side: (x + -2)(x + -2) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (x + -2) equal to 7.937253933 and -7.937253933.Subproblem 1
x + -2 = 7.937253933 Simplifying x + -2 = 7.937253933 Reorder the terms: -2 + x = 7.937253933 Solving -2 + x = 7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 7.937253933 + 2 Combine like terms: -2 + 2 = 0 0 + x = 7.937253933 + 2 x = 7.937253933 + 2 Combine like terms: 7.937253933 + 2 = 9.937253933 x = 9.937253933 Simplifying x = 9.937253933Subproblem 2
x + -2 = -7.937253933 Simplifying x + -2 = -7.937253933 Reorder the terms: -2 + x = -7.937253933 Solving -2 + x = -7.937253933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -7.937253933 + 2 Combine like terms: -2 + 2 = 0 0 + x = -7.937253933 + 2 x = -7.937253933 + 2 Combine like terms: -7.937253933 + 2 = -5.937253933 x = -5.937253933 Simplifying x = -5.937253933Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.937253933, -5.937253933}
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