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Simplifying -5x2 + -10x + 6 = 0 Reorder the terms: 6 + -10x + -5x2 = 0 Solving 6 + -10x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.2 + 2x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 2x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 2x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 2x + x2 = 0 + 1.2 2x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 2x + x2 = 1.2 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 1.2 + 1 Reorder the terms: 1 + 2x + x2 = 1.2 + 1 Combine like terms: 1.2 + 1 = 2.2 1 + 2x + x2 = 2.2 Factor a perfect square on the left side: (x + 1)(x + 1) = 2.2 Calculate the square root of the right side: 1.483239697 Break this problem into two subproblems by setting (x + 1) equal to 1.483239697 and -1.483239697.Subproblem 1
x + 1 = 1.483239697 Simplifying x + 1 = 1.483239697 Reorder the terms: 1 + x = 1.483239697 Solving 1 + x = 1.483239697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.483239697 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.483239697 + -1 x = 1.483239697 + -1 Combine like terms: 1.483239697 + -1 = 0.483239697 x = 0.483239697 Simplifying x = 0.483239697Subproblem 2
x + 1 = -1.483239697 Simplifying x + 1 = -1.483239697 Reorder the terms: 1 + x = -1.483239697 Solving 1 + x = -1.483239697 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.483239697 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.483239697 + -1 x = -1.483239697 + -1 Combine like terms: -1.483239697 + -1 = -2.483239697 x = -2.483239697 Simplifying x = -2.483239697Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.483239697, -2.483239697}
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