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Simplifying 10x2 + -5x + -6 = 0 Reorder the terms: -6 + -5x + 10x2 = 0 Solving -6 + -5x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.6 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -0.5x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + -0.5x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -0.5x + x2 = 0 + 0.6 -0.5x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 -0.5x + x2 = 0.6 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.6 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.6 + 0.0625 Combine like terms: 0.6 + 0.0625 = 0.6625 0.0625 + -0.5x + x2 = 0.6625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.6625 Calculate the square root of the right side: 0.81394103 Break this problem into two subproblems by setting (x + -0.25) equal to 0.81394103 and -0.81394103.Subproblem 1
x + -0.25 = 0.81394103 Simplifying x + -0.25 = 0.81394103 Reorder the terms: -0.25 + x = 0.81394103 Solving -0.25 + x = 0.81394103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.81394103 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.81394103 + 0.25 x = 0.81394103 + 0.25 Combine like terms: 0.81394103 + 0.25 = 1.06394103 x = 1.06394103 Simplifying x = 1.06394103Subproblem 2
x + -0.25 = -0.81394103 Simplifying x + -0.25 = -0.81394103 Reorder the terms: -0.25 + x = -0.81394103 Solving -0.25 + x = -0.81394103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.81394103 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.81394103 + 0.25 x = -0.81394103 + 0.25 Combine like terms: -0.81394103 + 0.25 = -0.56394103 x = -0.56394103 Simplifying x = -0.56394103Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.06394103, -0.56394103}
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