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Simplifying 6x2 + -6x = 7.75 Reorder the terms: -6x + 6x2 = 7.75 Solving -6x + 6x2 = 7.75 Solving for variable 'x'. Reorder the terms: -7.75 + -6x + 6x2 = 7.75 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 -7.75 + -6x + 6x2 = 0.00 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.291666667 + -1x + x2 = 0.00 Move the constant term to the right: Add '1.291666667' to each side of the equation. -1.291666667 + -1x + 1.291666667 + x2 = 0.00 + 1.291666667 Reorder the terms: -1.291666667 + 1.291666667 + -1x + x2 = 0.00 + 1.291666667 Combine like terms: -1.291666667 + 1.291666667 = 0.000000000 0.000000000 + -1x + x2 = 0.00 + 1.291666667 -1x + x2 = 0.00 + 1.291666667 Combine like terms: 0.00 + 1.291666667 = 1.291666667 -1x + x2 = 1.291666667 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1.291666667 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.291666667 + 0.25 Combine like terms: 1.291666667 + 0.25 = 1.541666667 0.25 + -1x + x2 = 1.541666667 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.541666667 Calculate the square root of the right side: 1.241638702 Break this problem into two subproblems by setting (x + -0.5) equal to 1.241638702 and -1.241638702.Subproblem 1
x + -0.5 = 1.241638702 Simplifying x + -0.5 = 1.241638702 Reorder the terms: -0.5 + x = 1.241638702 Solving -0.5 + x = 1.241638702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.241638702 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.241638702 + 0.5 x = 1.241638702 + 0.5 Combine like terms: 1.241638702 + 0.5 = 1.741638702 x = 1.741638702 Simplifying x = 1.741638702Subproblem 2
x + -0.5 = -1.241638702 Simplifying x + -0.5 = -1.241638702 Reorder the terms: -0.5 + x = -1.241638702 Solving -0.5 + x = -1.241638702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.241638702 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.241638702 + 0.5 x = -1.241638702 + 0.5 Combine like terms: -1.241638702 + 0.5 = -0.741638702 x = -0.741638702 Simplifying x = -0.741638702Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.741638702, -0.741638702}
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