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Simplifying 6x2 + -15x + -49 = 0 Reorder the terms: -49 + -15x + 6x2 = 0 Solving -49 + -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'. -8.166666667 + -2.5x + x2 = 0 Move the constant term to the right: Add '8.166666667' to each side of the equation. -8.166666667 + -2.5x + 8.166666667 + x2 = 0 + 8.166666667 Reorder the terms: -8.166666667 + 8.166666667 + -2.5x + x2 = 0 + 8.166666667 Combine like terms: -8.166666667 + 8.166666667 = 0.000000000 0.000000000 + -2.5x + x2 = 0 + 8.166666667 -2.5x + x2 = 0 + 8.166666667 Combine like terms: 0 + 8.166666667 = 8.166666667 -2.5x + x2 = 8.166666667 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 = 8.166666667 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 8.166666667 + 1.5625 Combine like terms: 8.166666667 + 1.5625 = 9.729166667 1.5625 + -2.5x + x2 = 9.729166667 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 9.729166667 Calculate the square root of the right side: 3.119161212 Break this problem into two subproblems by setting (x + -1.25) equal to 3.119161212 and -3.119161212.Subproblem 1
x + -1.25 = 3.119161212 Simplifying x + -1.25 = 3.119161212 Reorder the terms: -1.25 + x = 3.119161212 Solving -1.25 + x = 3.119161212 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 = 3.119161212 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 3.119161212 + 1.25 x = 3.119161212 + 1.25 Combine like terms: 3.119161212 + 1.25 = 4.369161212 x = 4.369161212 Simplifying x = 4.369161212Subproblem 2
x + -1.25 = -3.119161212 Simplifying x + -1.25 = -3.119161212 Reorder the terms: -1.25 + x = -3.119161212 Solving -1.25 + x = -3.119161212 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 = -3.119161212 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -3.119161212 + 1.25 x = -3.119161212 + 1.25 Combine like terms: -3.119161212 + 1.25 = -1.869161212 x = -1.869161212 Simplifying x = -1.869161212Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.369161212, -1.869161212}
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