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Simplifying x * 2x + -3x + 2 = 32 Reorder the terms for easier multiplication: 2x * x + -3x + 2 = 32 Multiply x * x 2x2 + -3x + 2 = 32 Reorder the terms: 2 + -3x + 2x2 = 32 Solving 2 + -3x + 2x2 = 32 Solving for variable 'x'. Reorder the terms: 2 + -32 + -3x + 2x2 = 32 + -32 Combine like terms: 2 + -32 = -30 -30 + -3x + 2x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -30 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -15 + -1.5x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -1.5x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -1.5x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1.5x + x2 = 0 + 15 -1.5x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -1.5x + x2 = 15 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 = 15 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 15 + 0.5625 Combine like terms: 15 + 0.5625 = 15.5625 0.5625 + -1.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + -0.75) equal to 3.94493346 and -3.94493346.Subproblem 1
x + -0.75 = 3.94493346 Simplifying x + -0.75 = 3.94493346 Reorder the terms: -0.75 + x = 3.94493346 Solving -0.75 + x = 3.94493346 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 = 3.94493346 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 3.94493346 + 0.75 x = 3.94493346 + 0.75 Combine like terms: 3.94493346 + 0.75 = 4.69493346 x = 4.69493346 Simplifying x = 4.69493346Subproblem 2
x + -0.75 = -3.94493346 Simplifying x + -0.75 = -3.94493346 Reorder the terms: -0.75 + x = -3.94493346 Solving -0.75 + x = -3.94493346 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 = -3.94493346 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -3.94493346 + 0.75 x = -3.94493346 + 0.75 Combine like terms: -3.94493346 + 0.75 = -3.19493346 x = -3.19493346 Simplifying x = -3.19493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.69493346, -3.19493346}
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