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Simplifying x2 = 3x + 32 Reorder the terms: x2 = 32 + 3x Solving x2 = 32 + 3x Solving for variable 'x'. Reorder the terms: -32 + -3x + x2 = 32 + 3x + -32 + -3x Reorder the terms: -32 + -3x + x2 = 32 + -32 + 3x + -3x Combine like terms: 32 + -32 = 0 -32 + -3x + x2 = 0 + 3x + -3x -32 + -3x + x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -32 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -3x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -3x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -3x + x2 = 0 + 32 -3x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -3x + x2 = 32 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 32 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 32 + 2.25 Combine like terms: 32 + 2.25 = 34.25 2.25 + -3x + x2 = 34.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 34.25 Calculate the square root of the right side: 5.852349955 Break this problem into two subproblems by setting (x + -1.5) equal to 5.852349955 and -5.852349955.Subproblem 1
x + -1.5 = 5.852349955 Simplifying x + -1.5 = 5.852349955 Reorder the terms: -1.5 + x = 5.852349955 Solving -1.5 + x = 5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 5.852349955 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 5.852349955 + 1.5 x = 5.852349955 + 1.5 Combine like terms: 5.852349955 + 1.5 = 7.352349955 x = 7.352349955 Simplifying x = 7.352349955Subproblem 2
x + -1.5 = -5.852349955 Simplifying x + -1.5 = -5.852349955 Reorder the terms: -1.5 + x = -5.852349955 Solving -1.5 + x = -5.852349955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -5.852349955 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -5.852349955 + 1.5 x = -5.852349955 + 1.5 Combine like terms: -5.852349955 + 1.5 = -4.352349955 x = -4.352349955 Simplifying x = -4.352349955Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.352349955, -4.352349955}
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