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Simplifying -6x2 + 10x + 14 = 5 Reorder the terms: 14 + 10x + -6x2 = 5 Solving 14 + 10x + -6x2 = 5 Solving for variable 'x'. Reorder the terms: 14 + -5 + 10x + -6x2 = 5 + -5 Combine like terms: 14 + -5 = 9 9 + 10x + -6x2 = 5 + -5 Combine like terms: 5 + -5 = 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 = 2.3146990695 x = 2.3146990695 Simplifying x = 2.3146990695Subproblem 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 = -0.6480324025 x = -0.6480324025 Simplifying x = -0.6480324025Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3146990695, -0.6480324025}
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