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Simplifying 15x2 + 22x = 8 Reorder the terms: 22x + 15x2 = 8 Solving 22x + 15x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + 22x + 15x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 22x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.5333333333 + 1.466666667x + x2 = 0 Move the constant term to the right: Add '0.5333333333' to each side of the equation. -0.5333333333 + 1.466666667x + 0.5333333333 + x2 = 0 + 0.5333333333 Reorder the terms: -0.5333333333 + 0.5333333333 + 1.466666667x + x2 = 0 + 0.5333333333 Combine like terms: -0.5333333333 + 0.5333333333 = 0.0000000000 0.0000000000 + 1.466666667x + x2 = 0 + 0.5333333333 1.466666667x + x2 = 0 + 0.5333333333 Combine like terms: 0 + 0.5333333333 = 0.5333333333 1.466666667x + x2 = 0.5333333333 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 = 0.5333333333 + 0.5377777780 Reorder the terms: 0.5377777780 + 1.466666667x + x2 = 0.5333333333 + 0.5377777780 Combine like terms: 0.5333333333 + 0.5377777780 = 1.0711111113 0.5377777780 + 1.466666667x + x2 = 1.0711111113 Factor a perfect square on the left side: (x + 0.7333333335)(x + 0.7333333335) = 1.0711111113 Calculate the square root of the right side: 1.03494498 Break this problem into two subproblems by setting (x + 0.7333333335) equal to 1.03494498 and -1.03494498.Subproblem 1
x + 0.7333333335 = 1.03494498 Simplifying x + 0.7333333335 = 1.03494498 Reorder the terms: 0.7333333335 + x = 1.03494498 Solving 0.7333333335 + x = 1.03494498 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 = 1.03494498 + -0.7333333335 Combine like terms: 0.7333333335 + -0.7333333335 = 0.0000000000 0.0000000000 + x = 1.03494498 + -0.7333333335 x = 1.03494498 + -0.7333333335 Combine like terms: 1.03494498 + -0.7333333335 = 0.3016116465 x = 0.3016116465 Simplifying x = 0.3016116465Subproblem 2
x + 0.7333333335 = -1.03494498 Simplifying x + 0.7333333335 = -1.03494498 Reorder the terms: 0.7333333335 + x = -1.03494498 Solving 0.7333333335 + x = -1.03494498 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 = -1.03494498 + -0.7333333335 Combine like terms: 0.7333333335 + -0.7333333335 = 0.0000000000 0.0000000000 + x = -1.03494498 + -0.7333333335 x = -1.03494498 + -0.7333333335 Combine like terms: -1.03494498 + -0.7333333335 = -1.7682783135 x = -1.7682783135 Simplifying x = -1.7682783135Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3016116465, -1.7682783135}
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