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Simplifying x2 + -4x + 6 + -3 = 36 Reorder the terms: 6 + -3 + -4x + x2 = 36 Combine like terms: 6 + -3 = 3 3 + -4x + x2 = 36 Solving 3 + -4x + x2 = 36 Solving for variable 'x'. Reorder the terms: 3 + -36 + -4x + x2 = 36 + -36 Combine like terms: 3 + -36 = -33 -33 + -4x + x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -33 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '33' to each side of the equation. -33 + -4x + 33 + x2 = 0 + 33 Reorder the terms: -33 + 33 + -4x + x2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -4x + x2 = 0 + 33 -4x + x2 = 0 + 33 Combine like terms: 0 + 33 = 33 -4x + x2 = 33 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 = 33 + 4 Reorder the terms: 4 + -4x + x2 = 33 + 4 Combine like terms: 33 + 4 = 37 4 + -4x + x2 = 37 Factor a perfect square on the left side: (x + -2)(x + -2) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (x + -2) equal to 6.08276253 and -6.08276253.Subproblem 1
x + -2 = 6.08276253 Simplifying x + -2 = 6.08276253 Reorder the terms: -2 + x = 6.08276253 Solving -2 + x = 6.08276253 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 = 6.08276253 + 2 Combine like terms: -2 + 2 = 0 0 + x = 6.08276253 + 2 x = 6.08276253 + 2 Combine like terms: 6.08276253 + 2 = 8.08276253 x = 8.08276253 Simplifying x = 8.08276253Subproblem 2
x + -2 = -6.08276253 Simplifying x + -2 = -6.08276253 Reorder the terms: -2 + x = -6.08276253 Solving -2 + x = -6.08276253 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 = -6.08276253 + 2 Combine like terms: -2 + 2 = 0 0 + x = -6.08276253 + 2 x = -6.08276253 + 2 Combine like terms: -6.08276253 + 2 = -4.08276253 x = -4.08276253 Simplifying x = -4.08276253Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.08276253, -4.08276253}
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