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Simplifying 4x2 + -3x2 + x + 5 = 32 Reorder the terms: 5 + x + 4x2 + -3x2 = 32 Combine like terms: 4x2 + -3x2 = 1x2 5 + x + 1x2 = 32 Solving 5 + x + 1x2 = 32 Solving for variable 'x'. Reorder the terms: 5 + -32 + x + 1x2 = 32 + -32 Combine like terms: 5 + -32 = -27 -27 + x + 1x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -27 + x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + x + x2 = 0 + 27 x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 x + x2 = 27 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 27 + 0.25 Reorder the terms: 0.25 + x + x2 = 27 + 0.25 Combine like terms: 27 + 0.25 = 27.25 0.25 + x + x2 = 27.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 27.25 Calculate the square root of the right side: 5.220153254 Break this problem into two subproblems by setting (x + 0.5) equal to 5.220153254 and -5.220153254.Subproblem 1
x + 0.5 = 5.220153254 Simplifying x + 0.5 = 5.220153254 Reorder the terms: 0.5 + x = 5.220153254 Solving 0.5 + x = 5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.220153254 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.220153254 + -0.5 x = 5.220153254 + -0.5 Combine like terms: 5.220153254 + -0.5 = 4.720153254 x = 4.720153254 Simplifying x = 4.720153254Subproblem 2
x + 0.5 = -5.220153254 Simplifying x + 0.5 = -5.220153254 Reorder the terms: 0.5 + x = -5.220153254 Solving 0.5 + x = -5.220153254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.220153254 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.220153254 + -0.5 x = -5.220153254 + -0.5 Combine like terms: -5.220153254 + -0.5 = -5.720153254 x = -5.720153254 Simplifying x = -5.720153254Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.720153254, -5.720153254}
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