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Simplifying 6x2 + -15x + 8 = 0 Reorder the terms: 8 + -15x + 6x2 = 0 Solving 8 + -15x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.333333333 + -2.5x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + -2.5x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + -2.5x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + -2.5x + x2 = 0 + -1.333333333 -2.5x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 -2.5x + x2 = -1.333333333 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = -1.333333333 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = -1.333333333 + 1.5625 Combine like terms: -1.333333333 + 1.5625 = 0.229166667 1.5625 + -2.5x + x2 = 0.229166667 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 0.229166667 Calculate the square root of the right side: 0.478713554 Break this problem into two subproblems by setting (x + -1.25) equal to 0.478713554 and -0.478713554.Subproblem 1
x + -1.25 = 0.478713554 Simplifying x + -1.25 = 0.478713554 Reorder the terms: -1.25 + x = 0.478713554 Solving -1.25 + x = 0.478713554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 0.478713554 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 0.478713554 + 1.25 x = 0.478713554 + 1.25 Combine like terms: 0.478713554 + 1.25 = 1.728713554 x = 1.728713554 Simplifying x = 1.728713554Subproblem 2
x + -1.25 = -0.478713554 Simplifying x + -1.25 = -0.478713554 Reorder the terms: -1.25 + x = -0.478713554 Solving -1.25 + x = -0.478713554 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -0.478713554 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -0.478713554 + 1.25 x = -0.478713554 + 1.25 Combine like terms: -0.478713554 + 1.25 = 0.771286446 x = 0.771286446 Simplifying x = 0.771286446Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.728713554, 0.771286446}
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