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Simplifying 6x2 = -10x + 9 Reorder the terms: 6x2 = 9 + -10x Solving 6x2 = 9 + -10x Solving for variable 'x'. Reorder the terms: -9 + 10x + 6x2 = 9 + -10x + -9 + 10x Reorder the terms: -9 + 10x + 6x2 = 9 + -9 + -10x + 10x Combine like terms: 9 + -9 = 0 -9 + 10x + 6x2 = 0 + -10x + 10x -9 + 10x + 6x2 = -10x + 10x Combine like terms: -10x + 10x = 0 -9 + 10x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.5 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 1.666666667x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 1.666666667x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 1.666666667x + x2 = 0 + 1.5 1.666666667x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 1.666666667x + x2 = 1.5 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = 1.5 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 1.5 + 0.6944444447 Combine like terms: 1.5 + 0.6944444447 = 2.1944444447 0.6944444447 + 1.666666667x + x2 = 2.1944444447 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 2.1944444447 Calculate the square root of the right side: 1.481365736 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 1.481365736 and -1.481365736.Subproblem 1
x + 0.8333333335 = 1.481365736 Simplifying x + 0.8333333335 = 1.481365736 Reorder the terms: 0.8333333335 + x = 1.481365736 Solving 0.8333333335 + x = 1.481365736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.481365736 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.481365736 + -0.8333333335 x = 1.481365736 + -0.8333333335 Combine like terms: 1.481365736 + -0.8333333335 = 0.6480324025 x = 0.6480324025 Simplifying x = 0.6480324025Subproblem 2
x + 0.8333333335 = -1.481365736 Simplifying x + 0.8333333335 = -1.481365736 Reorder the terms: 0.8333333335 + x = -1.481365736 Solving 0.8333333335 + x = -1.481365736 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.481365736 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.481365736 + -0.8333333335 x = -1.481365736 + -0.8333333335 Combine like terms: -1.481365736 + -0.8333333335 = -2.3146990695 x = -2.3146990695 Simplifying x = -2.3146990695Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6480324025, -2.3146990695}
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