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Simplifying 22 = x(2x + -3) Reorder the terms: 22 = x(-3 + 2x) 22 = (-3 * x + 2x * x) 22 = (-3x + 2x2) Solving 22 = -3x + 2x2 Solving for variable 'x'. Reorder the terms: 22 + 3x + -2x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 22 + 3x + -2x2 = 0 + 2x2 + -2x2 22 + 3x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 22 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -11 + -1.5x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -1.5x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -1.5x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1.5x + x2 = 0 + 11 -1.5x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -1.5x + x2 = 11 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 11 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 11 + 0.5625 Combine like terms: 11 + 0.5625 = 11.5625 0.5625 + -1.5x + x2 = 11.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (x + -0.75) equal to 3.400367627 and -3.400367627.Subproblem 1
x + -0.75 = 3.400367627 Simplifying x + -0.75 = 3.400367627 Reorder the terms: -0.75 + x = 3.400367627 Solving -0.75 + x = 3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 3.400367627 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 3.400367627 + 0.75 x = 3.400367627 + 0.75 Combine like terms: 3.400367627 + 0.75 = 4.150367627 x = 4.150367627 Simplifying x = 4.150367627Subproblem 2
x + -0.75 = -3.400367627 Simplifying x + -0.75 = -3.400367627 Reorder the terms: -0.75 + x = -3.400367627 Solving -0.75 + x = -3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -3.400367627 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -3.400367627 + 0.75 x = -3.400367627 + 0.75 Combine like terms: -3.400367627 + 0.75 = -2.650367627 x = -2.650367627 Simplifying x = -2.650367627Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.150367627, -2.650367627}
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