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Simplifying 15x2 + -22x + 6 = 0 Reorder the terms: 6 + -22x + 15x2 = 0 Solving 6 + -22x + 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 + -1.466666667x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -1.466666667x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -1.466666667x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -1.466666667x + x2 = 0 + -0.4 -1.466666667x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -1.466666667x + x2 = -0.4 The x term is -1.466666667x. Take half its coefficient (-0.7333333335). Square it (0.5377777780) and add it to both sides. Add '0.5377777780' to each side of the equation. -1.466666667x + 0.5377777780 + x2 = -0.4 + 0.5377777780 Reorder the terms: 0.5377777780 + -1.466666667x + x2 = -0.4 + 0.5377777780 Combine like terms: -0.4 + 0.5377777780 = 0.137777778 0.5377777780 + -1.466666667x + x2 = 0.137777778 Factor a perfect square on the left side: (x + -0.7333333335)(x + -0.7333333335) = 0.137777778 Calculate the square root of the right side: 0.371184291 Break this problem into two subproblems by setting (x + -0.7333333335) equal to 0.371184291 and -0.371184291.Subproblem 1
x + -0.7333333335 = 0.371184291 Simplifying x + -0.7333333335 = 0.371184291 Reorder the terms: -0.7333333335 + x = 0.371184291 Solving -0.7333333335 + x = 0.371184291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7333333335' to each side of the equation. -0.7333333335 + 0.7333333335 + x = 0.371184291 + 0.7333333335 Combine like terms: -0.7333333335 + 0.7333333335 = 0.0000000000 0.0000000000 + x = 0.371184291 + 0.7333333335 x = 0.371184291 + 0.7333333335 Combine like terms: 0.371184291 + 0.7333333335 = 1.1045176245 x = 1.1045176245 Simplifying x = 1.1045176245Subproblem 2
x + -0.7333333335 = -0.371184291 Simplifying x + -0.7333333335 = -0.371184291 Reorder the terms: -0.7333333335 + x = -0.371184291 Solving -0.7333333335 + x = -0.371184291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7333333335' to each side of the equation. -0.7333333335 + 0.7333333335 + x = -0.371184291 + 0.7333333335 Combine like terms: -0.7333333335 + 0.7333333335 = 0.0000000000 0.0000000000 + x = -0.371184291 + 0.7333333335 x = -0.371184291 + 0.7333333335 Combine like terms: -0.371184291 + 0.7333333335 = 0.3621490425 x = 0.3621490425 Simplifying x = 0.3621490425Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1045176245, 0.3621490425}
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