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Simplifying 5x2 + 10x + 2x = 2 Reorder the terms: 10x + 2x + 5x2 = 2 Combine like terms: 10x + 2x = 12x 12x + 5x2 = 2 Solving 12x + 5x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + 12x + 5x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 2.4x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 2.4x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 2.4x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 2.4x + x2 = 0 + 0.4 2.4x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 2.4x + x2 = 0.4 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = 0.4 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 0.4 + 1.44 Combine like terms: 0.4 + 1.44 = 1.84 1.44 + 2.4x + x2 = 1.84 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (x + 1.2) equal to 1.356465997 and -1.356465997.Subproblem 1
x + 1.2 = 1.356465997 Simplifying x + 1.2 = 1.356465997 Reorder the terms: 1.2 + x = 1.356465997 Solving 1.2 + x = 1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 1.356465997 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.356465997 + -1.2 x = 1.356465997 + -1.2 Combine like terms: 1.356465997 + -1.2 = 0.156465997 x = 0.156465997 Simplifying x = 0.156465997Subproblem 2
x + 1.2 = -1.356465997 Simplifying x + 1.2 = -1.356465997 Reorder the terms: 1.2 + x = -1.356465997 Solving 1.2 + x = -1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -1.356465997 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.356465997 + -1.2 x = -1.356465997 + -1.2 Combine like terms: -1.356465997 + -1.2 = -2.556465997 x = -2.556465997 Simplifying x = -2.556465997Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.156465997, -2.556465997}
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