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Simplifying 0.75x2 + 11x + -18 = 0 Reorder the terms: -18 + 11x + 0.75x2 = 0 Solving -18 + 11x + 0.75x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.75 the coefficient of the squared term: Divide each side by '0.75'. -24 + 14.66666667x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 14.66666667x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 14.66666667x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 14.66666667x + x2 = 0 + 24 14.66666667x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 14.66666667x + x2 = 24 The x term is 14.66666667x. Take half its coefficient (7.333333335). Square it (53.77777780) and add it to both sides. Add '53.77777780' to each side of the equation. 14.66666667x + 53.77777780 + x2 = 24 + 53.77777780 Reorder the terms: 53.77777780 + 14.66666667x + x2 = 24 + 53.77777780 Combine like terms: 24 + 53.77777780 = 77.7777778 53.77777780 + 14.66666667x + x2 = 77.7777778 Factor a perfect square on the left side: (x + 7.333333335)(x + 7.333333335) = 77.7777778 Calculate the square root of the right side: 8.819171038 Break this problem into two subproblems by setting (x + 7.333333335) equal to 8.819171038 and -8.819171038.Subproblem 1
x + 7.333333335 = 8.819171038 Simplifying x + 7.333333335 = 8.819171038 Reorder the terms: 7.333333335 + x = 8.819171038 Solving 7.333333335 + x = 8.819171038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + x = 8.819171038 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + x = 8.819171038 + -7.333333335 x = 8.819171038 + -7.333333335 Combine like terms: 8.819171038 + -7.333333335 = 1.485837703 x = 1.485837703 Simplifying x = 1.485837703Subproblem 2
x + 7.333333335 = -8.819171038 Simplifying x + 7.333333335 = -8.819171038 Reorder the terms: 7.333333335 + x = -8.819171038 Solving 7.333333335 + x = -8.819171038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + x = -8.819171038 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + x = -8.819171038 + -7.333333335 x = -8.819171038 + -7.333333335 Combine like terms: -8.819171038 + -7.333333335 = -16.152504373 x = -16.152504373 Simplifying x = -16.152504373Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.485837703, -16.152504373}
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