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Simplifying 5x2 + 3x + 2 = x + 6 Reorder the terms: 2 + 3x + 5x2 = x + 6 Reorder the terms: 2 + 3x + 5x2 = 6 + x Solving 2 + 3x + 5x2 = 6 + x Solving for variable 'x'. Reorder the terms: 2 + -6 + 3x + -1x + 5x2 = 6 + x + -6 + -1x Combine like terms: 2 + -6 = -4 -4 + 3x + -1x + 5x2 = 6 + x + -6 + -1x Combine like terms: 3x + -1x = 2x -4 + 2x + 5x2 = 6 + x + -6 + -1x Reorder the terms: -4 + 2x + 5x2 = 6 + -6 + x + -1x Combine like terms: 6 + -6 = 0 -4 + 2x + 5x2 = 0 + x + -1x -4 + 2x + 5x2 = x + -1x Combine like terms: x + -1x = 0 -4 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.8 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.8' to each side of the equation. -0.8 + 0.4x + 0.8 + x2 = 0 + 0.8 Reorder the terms: -0.8 + 0.8 + 0.4x + x2 = 0 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + 0.4x + x2 = 0 + 0.8 0.4x + x2 = 0 + 0.8 Combine like terms: 0 + 0.8 = 0.8 0.4x + x2 = 0.8 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.8 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.8 + 0.04 Combine like terms: 0.8 + 0.04 = 0.84 0.04 + 0.4x + x2 = 0.84 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.84 Calculate the square root of the right side: 0.916515139 Break this problem into two subproblems by setting (x + 0.2) equal to 0.916515139 and -0.916515139.Subproblem 1
x + 0.2 = 0.916515139 Simplifying x + 0.2 = 0.916515139 Reorder the terms: 0.2 + x = 0.916515139 Solving 0.2 + x = 0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.916515139 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.916515139 + -0.2 x = 0.916515139 + -0.2 Combine like terms: 0.916515139 + -0.2 = 0.716515139 x = 0.716515139 Simplifying x = 0.716515139Subproblem 2
x + 0.2 = -0.916515139 Simplifying x + 0.2 = -0.916515139 Reorder the terms: 0.2 + x = -0.916515139 Solving 0.2 + x = -0.916515139 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.916515139 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.916515139 + -0.2 x = -0.916515139 + -0.2 Combine like terms: -0.916515139 + -0.2 = -1.116515139 x = -1.116515139 Simplifying x = -1.116515139Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.716515139, -1.116515139}
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