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Simplifying 15x2 + 11x + -6 = 0 Reorder the terms: -6 + 11x + 15x2 = 0 Solving -6 + 11x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.4 + 0.7333333333x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.7333333333x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.7333333333x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.7333333333x + x2 = 0 + 0.4 0.7333333333x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.7333333333x + x2 = 0.4 The x term is 0.7333333333x. Take half its coefficient (0.3666666667). Square it (0.1344444445) and add it to both sides. Add '0.1344444445' to each side of the equation. 0.7333333333x + 0.1344444445 + x2 = 0.4 + 0.1344444445 Reorder the terms: 0.1344444445 + 0.7333333333x + x2 = 0.4 + 0.1344444445 Combine like terms: 0.4 + 0.1344444445 = 0.5344444445 0.1344444445 + 0.7333333333x + x2 = 0.5344444445 Factor a perfect square on the left side: (x + 0.3666666667)(x + 0.3666666667) = 0.5344444445 Calculate the square root of the right side: 0.731057073 Break this problem into two subproblems by setting (x + 0.3666666667) equal to 0.731057073 and -0.731057073.Subproblem 1
x + 0.3666666667 = 0.731057073 Simplifying x + 0.3666666667 = 0.731057073 Reorder the terms: 0.3666666667 + x = 0.731057073 Solving 0.3666666667 + x = 0.731057073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3666666667' to each side of the equation. 0.3666666667 + -0.3666666667 + x = 0.731057073 + -0.3666666667 Combine like terms: 0.3666666667 + -0.3666666667 = 0.0000000000 0.0000000000 + x = 0.731057073 + -0.3666666667 x = 0.731057073 + -0.3666666667 Combine like terms: 0.731057073 + -0.3666666667 = 0.3643904063 x = 0.3643904063 Simplifying x = 0.3643904063Subproblem 2
x + 0.3666666667 = -0.731057073 Simplifying x + 0.3666666667 = -0.731057073 Reorder the terms: 0.3666666667 + x = -0.731057073 Solving 0.3666666667 + x = -0.731057073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3666666667' to each side of the equation. 0.3666666667 + -0.3666666667 + x = -0.731057073 + -0.3666666667 Combine like terms: 0.3666666667 + -0.3666666667 = 0.0000000000 0.0000000000 + x = -0.731057073 + -0.3666666667 x = -0.731057073 + -0.3666666667 Combine like terms: -0.731057073 + -0.3666666667 = -1.0977237397 x = -1.0977237397 Simplifying x = -1.0977237397Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3643904063, -1.0977237397}
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