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Simplifying 5x2 + 2x + 6 = 12 Reorder the terms: 6 + 2x + 5x2 = 12 Solving 6 + 2x + 5x2 = 12 Solving for variable 'x'. Reorder the terms: 6 + -12 + 2x + 5x2 = 12 + -12 Combine like terms: 6 + -12 = -6 -6 + 2x + 5x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -6 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + 0.4x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 0.4x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 0.4x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 0.4x + x2 = 0 + 1.2 0.4x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 0.4x + x2 = 1.2 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 = 1.2 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 1.2 + 0.04 Combine like terms: 1.2 + 0.04 = 1.24 0.04 + 0.4x + x2 = 1.24 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 1.24 Calculate the square root of the right side: 1.113552873 Break this problem into two subproblems by setting (x + 0.2) equal to 1.113552873 and -1.113552873.Subproblem 1
x + 0.2 = 1.113552873 Simplifying x + 0.2 = 1.113552873 Reorder the terms: 0.2 + x = 1.113552873 Solving 0.2 + x = 1.113552873 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 = 1.113552873 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.113552873 + -0.2 x = 1.113552873 + -0.2 Combine like terms: 1.113552873 + -0.2 = 0.913552873 x = 0.913552873 Simplifying x = 0.913552873Subproblem 2
x + 0.2 = -1.113552873 Simplifying x + 0.2 = -1.113552873 Reorder the terms: 0.2 + x = -1.113552873 Solving 0.2 + x = -1.113552873 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 = -1.113552873 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.113552873 + -0.2 x = -1.113552873 + -0.2 Combine like terms: -1.113552873 + -0.2 = -1.313552873 x = -1.313552873 Simplifying x = -1.313552873Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.913552873, -1.313552873}
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