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Simplifying 5x2 + -12x = 11 Reorder the terms: -12x + 5x2 = 11 Solving -12x + 5x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -12x + 5x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.2 + -2.4x + x2 = 0 Move the constant term to the right: Add '2.2' to each side of the equation. -2.2 + -2.4x + 2.2 + x2 = 0 + 2.2 Reorder the terms: -2.2 + 2.2 + -2.4x + x2 = 0 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + -2.4x + x2 = 0 + 2.2 -2.4x + x2 = 0 + 2.2 Combine like terms: 0 + 2.2 = 2.2 -2.4x + x2 = 2.2 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 = 2.2 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 2.2 + 1.44 Combine like terms: 2.2 + 1.44 = 3.64 1.44 + -2.4x + x2 = 3.64 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 3.64 Calculate the square root of the right side: 1.907878403 Break this problem into two subproblems by setting (x + -1.2) equal to 1.907878403 and -1.907878403.Subproblem 1
x + -1.2 = 1.907878403 Simplifying x + -1.2 = 1.907878403 Reorder the terms: -1.2 + x = 1.907878403 Solving -1.2 + x = 1.907878403 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 = 1.907878403 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.907878403 + 1.2 x = 1.907878403 + 1.2 Combine like terms: 1.907878403 + 1.2 = 3.107878403 x = 3.107878403 Simplifying x = 3.107878403Subproblem 2
x + -1.2 = -1.907878403 Simplifying x + -1.2 = -1.907878403 Reorder the terms: -1.2 + x = -1.907878403 Solving -1.2 + x = -1.907878403 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 = -1.907878403 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.907878403 + 1.2 x = -1.907878403 + 1.2 Combine like terms: -1.907878403 + 1.2 = -0.707878403 x = -0.707878403 Simplifying x = -0.707878403Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.107878403, -0.707878403}
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