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Simplifying (3 + -1x)(-3 + x) + 10 = 0 Multiply (3 + -1x) * (-3 + x) (3(-3 + x) + -1x * (-3 + x)) + 10 = 0 ((-3 * 3 + x * 3) + -1x * (-3 + x)) + 10 = 0 ((-9 + 3x) + -1x * (-3 + x)) + 10 = 0 (-9 + 3x + (-3 * -1x + x * -1x)) + 10 = 0 (-9 + 3x + (3x + -1x2)) + 10 = 0 Combine like terms: 3x + 3x = 6x (-9 + 6x + -1x2) + 10 = 0 Reorder the terms: -9 + 10 + 6x + -1x2 = 0 Combine like terms: -9 + 10 = 1 1 + 6x + -1x2 = 0 Solving 1 + 6x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + -6x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -6x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -6x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -6x + x2 = 0 + 1 -6x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -6x + x2 = 1 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 1 + 9 Reorder the terms: 9 + -6x + x2 = 1 + 9 Combine like terms: 1 + 9 = 10 9 + -6x + x2 = 10 Factor a perfect square on the left side: (x + -3)(x + -3) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -3) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -3 = 3.16227766 Simplifying x + -3 = 3.16227766 Reorder the terms: -3 + x = 3.16227766 Solving -3 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.16227766 + 3 x = 3.16227766 + 3 Combine like terms: 3.16227766 + 3 = 6.16227766 x = 6.16227766 Simplifying x = 6.16227766Subproblem 2
x + -3 = -3.16227766 Simplifying x + -3 = -3.16227766 Reorder the terms: -3 + x = -3.16227766 Solving -3 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.16227766 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.16227766 + 3 x = -3.16227766 + 3 Combine like terms: -3.16227766 + 3 = -0.16227766 x = -0.16227766 Simplifying x = -0.16227766Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.16227766, -0.16227766}
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