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Simplifying 15x2 + -35 = -22x Reorder the terms: -35 + 15x2 = -22x Solving -35 + 15x2 = -22x Solving for variable 'x'. Reorder the terms: -35 + 22x + 15x2 = -22x + 22x Combine like terms: -22x + 22x = 0 -35 + 22x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -2.333333333 + 1.466666667x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + 1.466666667x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + 1.466666667x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + 1.466666667x + x2 = 0 + 2.333333333 1.466666667x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 1.466666667x + x2 = 2.333333333 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 = 2.333333333 + 0.5377777780 Reorder the terms: 0.5377777780 + 1.466666667x + x2 = 2.333333333 + 0.5377777780 Combine like terms: 2.333333333 + 0.5377777780 = 2.871111111 0.5377777780 + 1.466666667x + x2 = 2.871111111 Factor a perfect square on the left side: (x + 0.7333333335)(x + 0.7333333335) = 2.871111111 Calculate the square root of the right side: 1.694435337 Break this problem into two subproblems by setting (x + 0.7333333335) equal to 1.694435337 and -1.694435337.Subproblem 1
x + 0.7333333335 = 1.694435337 Simplifying x + 0.7333333335 = 1.694435337 Reorder the terms: 0.7333333335 + x = 1.694435337 Solving 0.7333333335 + x = 1.694435337 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 = 1.694435337 + -0.7333333335 Combine like terms: 0.7333333335 + -0.7333333335 = 0.0000000000 0.0000000000 + x = 1.694435337 + -0.7333333335 x = 1.694435337 + -0.7333333335 Combine like terms: 1.694435337 + -0.7333333335 = 0.9611020035 x = 0.9611020035 Simplifying x = 0.9611020035Subproblem 2
x + 0.7333333335 = -1.694435337 Simplifying x + 0.7333333335 = -1.694435337 Reorder the terms: 0.7333333335 + x = -1.694435337 Solving 0.7333333335 + x = -1.694435337 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 = -1.694435337 + -0.7333333335 Combine like terms: 0.7333333335 + -0.7333333335 = 0.0000000000 0.0000000000 + x = -1.694435337 + -0.7333333335 x = -1.694435337 + -0.7333333335 Combine like terms: -1.694435337 + -0.7333333335 = -2.4277686705 x = -2.4277686705 Simplifying x = -2.4277686705Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9611020035, -2.4277686705}
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