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Simplifying 4x2 + 21x + -6 = 0 Reorder the terms: -6 + 21x + 4x2 = 0 Solving -6 + 21x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.5 + 5.25x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 5.25x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 5.25x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 5.25x + x2 = 0 + 1.5 5.25x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 5.25x + x2 = 1.5 The x term is 5.25x. Take half its coefficient (2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. 5.25x + 6.890625 + x2 = 1.5 + 6.890625 Reorder the terms: 6.890625 + 5.25x + x2 = 1.5 + 6.890625 Combine like terms: 1.5 + 6.890625 = 8.390625 6.890625 + 5.25x + x2 = 8.390625 Factor a perfect square on the left side: (x + 2.625)(x + 2.625) = 8.390625 Calculate the square root of the right side: 2.896657557 Break this problem into two subproblems by setting (x + 2.625) equal to 2.896657557 and -2.896657557.Subproblem 1
x + 2.625 = 2.896657557 Simplifying x + 2.625 = 2.896657557 Reorder the terms: 2.625 + x = 2.896657557 Solving 2.625 + x = 2.896657557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = 2.896657557 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = 2.896657557 + -2.625 x = 2.896657557 + -2.625 Combine like terms: 2.896657557 + -2.625 = 0.271657557 x = 0.271657557 Simplifying x = 0.271657557Subproblem 2
x + 2.625 = -2.896657557 Simplifying x + 2.625 = -2.896657557 Reorder the terms: 2.625 + x = -2.896657557 Solving 2.625 + x = -2.896657557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + x = -2.896657557 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + x = -2.896657557 + -2.625 x = -2.896657557 + -2.625 Combine like terms: -2.896657557 + -2.625 = -5.521657557 x = -5.521657557 Simplifying x = -5.521657557Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.271657557, -5.521657557}
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