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Simplifying 6 + 8x2 + -1x = 18x2 Reorder the terms: 6 + -1x + 8x2 = 18x2 Solving 6 + -1x + 8x2 = 18x2 Solving for variable 'x'. Combine like terms: 8x2 + -18x2 = -10x2 6 + -1x + -10x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 6 + -1x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -0.6 + 0.1x + x2 = 0.0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 0.1x + 0.6 + x2 = 0.0 + 0.6 Reorder the terms: -0.6 + 0.6 + 0.1x + x2 = 0.0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 0.1x + x2 = 0.0 + 0.6 0.1x + x2 = 0.0 + 0.6 Combine like terms: 0.0 + 0.6 = 0.6 0.1x + x2 = 0.6 The x term is 0.1x. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1x + 0.0025 + x2 = 0.6 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 0.6 + 0.0025 Combine like terms: 0.6 + 0.0025 = 0.6025 0.0025 + 0.1x + x2 = 0.6025 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 0.6025 Calculate the square root of the right side: 0.776208735 Break this problem into two subproblems by setting (x + 0.05) equal to 0.776208735 and -0.776208735.Subproblem 1
x + 0.05 = 0.776208735 Simplifying x + 0.05 = 0.776208735 Reorder the terms: 0.05 + x = 0.776208735 Solving 0.05 + x = 0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = 0.776208735 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.776208735 + -0.05 x = 0.776208735 + -0.05 Combine like terms: 0.776208735 + -0.05 = 0.726208735 x = 0.726208735 Simplifying x = 0.726208735Subproblem 2
x + 0.05 = -0.776208735 Simplifying x + 0.05 = -0.776208735 Reorder the terms: 0.05 + x = -0.776208735 Solving 0.05 + x = -0.776208735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = -0.776208735 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.776208735 + -0.05 x = -0.776208735 + -0.05 Combine like terms: -0.776208735 + -0.05 = -0.826208735 x = -0.826208735 Simplifying x = -0.826208735Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.726208735, -0.826208735}
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