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Simplifying 0.116 + 0.844x = x2 Solving 0.116 + 0.844x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 0.116 + 0.844x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.116 + -0.844x + x2 = 0 Move the constant term to the right: Add '0.116' to each side of the equation. -0.116 + -0.844x + 0.116 + x2 = 0 + 0.116 Reorder the terms: -0.116 + 0.116 + -0.844x + x2 = 0 + 0.116 Combine like terms: -0.116 + 0.116 = 0.000 0.000 + -0.844x + x2 = 0 + 0.116 -0.844x + x2 = 0 + 0.116 Combine like terms: 0 + 0.116 = 0.116 -0.844x + x2 = 0.116 The x term is -0.844x. Take half its coefficient (-0.422). Square it (0.178084) and add it to both sides. Add '0.178084' to each side of the equation. -0.844x + 0.178084 + x2 = 0.116 + 0.178084 Reorder the terms: 0.178084 + -0.844x + x2 = 0.116 + 0.178084 Combine like terms: 0.116 + 0.178084 = 0.294084 0.178084 + -0.844x + x2 = 0.294084 Factor a perfect square on the left side: (x + -0.422)(x + -0.422) = 0.294084 Calculate the square root of the right side: 0.542295123 Break this problem into two subproblems by setting (x + -0.422) equal to 0.542295123 and -0.542295123.Subproblem 1
x + -0.422 = 0.542295123 Simplifying x + -0.422 = 0.542295123 Reorder the terms: -0.422 + x = 0.542295123 Solving -0.422 + x = 0.542295123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.422' to each side of the equation. -0.422 + 0.422 + x = 0.542295123 + 0.422 Combine like terms: -0.422 + 0.422 = 0.000 0.000 + x = 0.542295123 + 0.422 x = 0.542295123 + 0.422 Combine like terms: 0.542295123 + 0.422 = 0.964295123 x = 0.964295123 Simplifying x = 0.964295123Subproblem 2
x + -0.422 = -0.542295123 Simplifying x + -0.422 = -0.542295123 Reorder the terms: -0.422 + x = -0.542295123 Solving -0.422 + x = -0.542295123 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.422' to each side of the equation. -0.422 + 0.422 + x = -0.542295123 + 0.422 Combine like terms: -0.422 + 0.422 = 0.000 0.000 + x = -0.542295123 + 0.422 x = -0.542295123 + 0.422 Combine like terms: -0.542295123 + 0.422 = -0.120295123 x = -0.120295123 Simplifying x = -0.120295123Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.964295123, -0.120295123}
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