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Simplifying 5x2 + 2x + -10 = 11 Reorder the terms: -10 + 2x + 5x2 = 11 Solving -10 + 2x + 5x2 = 11 Solving for variable 'x'. Reorder the terms: -10 + -11 + 2x + 5x2 = 11 + -11 Combine like terms: -10 + -11 = -21 -21 + 2x + 5x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -21 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + 0.4x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 0.4x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 0.4x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 0.4x + x2 = 0 + 4.2 0.4x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 0.4x + x2 = 4.2 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 = 4.2 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 4.2 + 0.04 Combine like terms: 4.2 + 0.04 = 4.24 0.04 + 0.4x + x2 = 4.24 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 4.24 Calculate the square root of the right side: 2.059126028 Break this problem into two subproblems by setting (x + 0.2) equal to 2.059126028 and -2.059126028.Subproblem 1
x + 0.2 = 2.059126028 Simplifying x + 0.2 = 2.059126028 Reorder the terms: 0.2 + x = 2.059126028 Solving 0.2 + x = 2.059126028 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 = 2.059126028 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 2.059126028 + -0.2 x = 2.059126028 + -0.2 Combine like terms: 2.059126028 + -0.2 = 1.859126028 x = 1.859126028 Simplifying x = 1.859126028Subproblem 2
x + 0.2 = -2.059126028 Simplifying x + 0.2 = -2.059126028 Reorder the terms: 0.2 + x = -2.059126028 Solving 0.2 + x = -2.059126028 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 = -2.059126028 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -2.059126028 + -0.2 x = -2.059126028 + -0.2 Combine like terms: -2.059126028 + -0.2 = -2.259126028 x = -2.259126028 Simplifying x = -2.259126028Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.859126028, -2.259126028}
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