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Simplifying 5x2 = 9 + -2x Solving 5x2 = 9 + -2x Solving for variable 'x'. Reorder the terms: -9 + 2x + 5x2 = 9 + -2x + -9 + 2x Reorder the terms: -9 + 2x + 5x2 = 9 + -9 + -2x + 2x Combine like terms: 9 + -9 = 0 -9 + 2x + 5x2 = 0 + -2x + 2x -9 + 2x + 5x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -9 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.8 + 0.4x + x2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + 0.4x + 1.8 + x2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + 0.4x + x2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + 0.4x + x2 = 0 + 1.8 0.4x + x2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 0.4x + x2 = 1.8 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 = 1.8 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 1.8 + 0.04 Combine like terms: 1.8 + 0.04 = 1.84 0.04 + 0.4x + x2 = 1.84 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (x + 0.2) equal to 1.356465997 and -1.356465997.Subproblem 1
x + 0.2 = 1.356465997 Simplifying x + 0.2 = 1.356465997 Reorder the terms: 0.2 + x = 1.356465997 Solving 0.2 + x = 1.356465997 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 = 1.356465997 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.356465997 + -0.2 x = 1.356465997 + -0.2 Combine like terms: 1.356465997 + -0.2 = 1.156465997 x = 1.156465997 Simplifying x = 1.156465997Subproblem 2
x + 0.2 = -1.356465997 Simplifying x + 0.2 = -1.356465997 Reorder the terms: 0.2 + x = -1.356465997 Solving 0.2 + x = -1.356465997 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 = -1.356465997 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.356465997 + -0.2 x = -1.356465997 + -0.2 Combine like terms: -1.356465997 + -0.2 = -1.556465997 x = -1.556465997 Simplifying x = -1.556465997Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.156465997, -1.556465997}
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