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Simplifying 0 = -6x2 + 10x + 5 Reorder the terms: 0 = 5 + 10x + -6x2 Solving 0 = 5 + 10x + -6x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -10x + 6x2 = 5 + 10x + -6x2 + -5 + -10x + 6x2 Reorder the terms: -5 + -10x + 6x2 = 5 + -5 + 10x + -10x + -6x2 + 6x2 Combine like terms: 5 + -5 = 0 -5 + -10x + 6x2 = 0 + 10x + -10x + -6x2 + 6x2 -5 + -10x + 6x2 = 10x + -10x + -6x2 + 6x2 Combine like terms: 10x + -10x = 0 -5 + -10x + 6x2 = 0 + -6x2 + 6x2 -5 + -10x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -5 + -10x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -1.666666667x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -1.666666667x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -1.666666667x + x2 = 0 + 0.8333333333 -1.666666667x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -1.666666667x + x2 = 0.8333333333 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 = 0.8333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 0.8333333333 + 0.6944444447 Combine like terms: 0.8333333333 + 0.6944444447 = 1.527777778 0.6944444447 + -1.666666667x + x2 = 1.527777778 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 1.527777778 Calculate the square root of the right side: 1.236033081 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.236033081 and -1.236033081.Subproblem 1
x + -0.8333333335 = 1.236033081 Simplifying x + -0.8333333335 = 1.236033081 Reorder the terms: -0.8333333335 + x = 1.236033081 Solving -0.8333333335 + x = 1.236033081 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 = 1.236033081 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.236033081 + 0.8333333335 x = 1.236033081 + 0.8333333335 Combine like terms: 1.236033081 + 0.8333333335 = 2.0693664145 x = 2.0693664145 Simplifying x = 2.0693664145Subproblem 2
x + -0.8333333335 = -1.236033081 Simplifying x + -0.8333333335 = -1.236033081 Reorder the terms: -0.8333333335 + x = -1.236033081 Solving -0.8333333335 + x = -1.236033081 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 = -1.236033081 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.236033081 + 0.8333333335 x = -1.236033081 + 0.8333333335 Combine like terms: -1.236033081 + 0.8333333335 = -0.4026997475 x = -0.4026997475 Simplifying x = -0.4026997475Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0693664145, -0.4026997475}
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