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Simplifying 6x2 + 15x + 7 = 0 Reorder the terms: 7 + 15x + 6x2 = 0 Solving 7 + 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'. 1.166666667 + 2.5x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + 2.5x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + 2.5x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + 2.5x + x2 = 0 + -1.166666667 2.5x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 2.5x + x2 = -1.166666667 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 = -1.166666667 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -1.166666667 + 1.5625 Combine like terms: -1.166666667 + 1.5625 = 0.395833333 1.5625 + 2.5x + x2 = 0.395833333 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 0.395833333 Calculate the square root of the right side: 0.629152869 Break this problem into two subproblems by setting (x + 1.25) equal to 0.629152869 and -0.629152869.Subproblem 1
x + 1.25 = 0.629152869 Simplifying x + 1.25 = 0.629152869 Reorder the terms: 1.25 + x = 0.629152869 Solving 1.25 + x = 0.629152869 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 = 0.629152869 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 0.629152869 + -1.25 x = 0.629152869 + -1.25 Combine like terms: 0.629152869 + -1.25 = -0.620847131 x = -0.620847131 Simplifying x = -0.620847131Subproblem 2
x + 1.25 = -0.629152869 Simplifying x + 1.25 = -0.629152869 Reorder the terms: 1.25 + x = -0.629152869 Solving 1.25 + x = -0.629152869 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 = -0.629152869 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -0.629152869 + -1.25 x = -0.629152869 + -1.25 Combine like terms: -0.629152869 + -1.25 = -1.879152869 x = -1.879152869 Simplifying x = -1.879152869Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.620847131, -1.879152869}
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